{"id":8813,"date":"2022-01-14T18:20:30","date_gmt":"2022-01-14T12:50:30","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=8813"},"modified":"2025-07-31T17:12:17","modified_gmt":"2025-07-31T11:42:17","slug":"ncert-solutions-for-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-5","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/","title":{"rendered":"NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#Class_7_Maths_Chapter_6_Exercise_65_Solution_-_Triangle_and_Its_Properties\" title=\"Class 7 Maths Chapter 6 Exercise 6.5 Solution &#8211; Triangle and Its Properties\">Class 7 Maths Chapter 6 Exercise 6.5 Solution &#8211; Triangle and Its Properties<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#NCERT_Solutions_for_Class_7_Maths_Chapter_6_Exercise_65_Updated_for_2024-25\" title=\"NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 Updated for 2024-25\">NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 Updated for 2024-25<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#NCERT_Solutions_for_Class_7_Maths_Chapter_6_Exercise_65_PDF_Download\" title=\"NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 PDF Download\">NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 PDF Download<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#FAQs_on_NCERT_Solutions_for_Class_7_Maths_Chapter_6_Exercise_65\" title=\"FAQs on NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5\">FAQs on NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#What_is_Pythagoras_theorem_in_Chapter_6_The_Triangle_and_its_Properties_of_Exercise_65_in_NCERT_Class_7_Maths\" title=\"What is Pythagoras&#039; theorem in Chapter 6 The Triangle and its Properties of Exercise 6.5 in NCERT Class 7 Maths?\">What is Pythagoras&#039; theorem in Chapter 6 The Triangle and its Properties of Exercise 6.5 in NCERT Class 7 Maths?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#How_will_the_final_exams_benefit_from_using_the_NCERT_Solutions_for_Class_7_Maths_Chapter_6_The_Triangle_and_its_Properties_Exercise_65\" title=\"How will the final exams benefit from using the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5)?\">How will the final exams benefit from using the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5)?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#What_is_a_Rhombus_in_Class_7_Maths_Chapter_6_The_Triangle_and_its_Properties\" title=\"What is a Rhombus in Class 7 Maths Chapter 6 The Triangle and its Properties?\">What is a Rhombus in Class 7 Maths Chapter 6 The Triangle and its Properties?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#What_is_a_Rectangle_in_Class_7_Maths_Chapter_6_The_Triangle_and_its_Properties\" title=\"What is a Rectangle in Class 7 Maths Chapter 6 The Triangle and its Properties?\">What is a Rectangle in Class 7 Maths Chapter 6 The Triangle and its Properties?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/chapter-6\/the-triangle-and-its-properties\/ex-6.5\/#Where_can_I_find_the_most_up-to-date_NCERT_Solutions_for_Class_7_Maths_Chapter_6_The_Triangle_and_its_Properties_Exercise_65\" title=\"Where can I find the most up-to-date NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5)?\">Where can I find the most up-to-date NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5)?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Class_7_Maths_Chapter_6_Exercise_65_Solution_-_Triangle_and_Its_Properties\"><\/span>Class 7 Maths Chapter 6 Exercise 6.5 Solution &#8211; Triangle and Its Properties<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The NCERT solutions for Class 7 Maths Chapter 6 Exercise 6.5, get into the fundamentals of triangles, encompassing Pythagoras&#8217; theorem and the angle sum property. These <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT solutions<\/strong><\/a>, aligned with the <a href=\"https:\/\/infinitylearn.com\/surge\/cbse\/cbse-syllabus\/\"><strong>CBSE syllabus<\/strong><\/a> and <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-books\/\"><strong>NCERT textbook<\/strong><\/a>, provide essential insights:<\/p>\n<ul>\n<li>Pythagoras&#8217; theorem elucidates that in a right-angled triangle, the square of the hypotenuse (the longest side) equals the sum of the squares of the other two sides.<\/li>\n<li>The converse of Pythagoras&#8217; theorem, a critical aspect covered in <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/maths\/\"><strong>NCERT solutions for Class 7 Maths<\/strong><\/a> Chapter 6, aids in determining whether a given triangle is right-angled. If the lengths of the sides (a, b, and c) satisfy the equation a\u00b2 + b\u00b2 = c\u00b2, the triangle qualifies as right-angled.<\/li>\n<li>Pythagorean triplets, highlighted in NCERT solutions for Class 7 Maths Chapter 6, are trios of positive integers (a, b, and c) satisfying the equation c\u00b2 = a\u00b2 + b\u00b2. Examples, like (3, 4, 5), (5, 12, 13), and (8, 15, 17), illustrate this concept.<\/li>\n<li>The angle sum property, another pivotal concept addressed in NCERT solutions for Class 7 Maths Chapter 6, asserts that the total sum of angles in any triangle invariably amounts to 180 degrees. This property serves as a cornerstone for resolving diverse triangle-related problems.<\/li>\n<li>Additionally, these <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/\"><strong>NCERT solutions for class 7<\/strong><\/a> gets into various other triangle properties, elucidating the interplay between sides and angles and providing methodologies for determining unknown angles or sides based on given information.<\/li>\n<\/ul>\n<p>By thoroughly grasping the concepts delineated in these NCERT solutions for Class 7 Maths Chapter 6, students can construct a robust foundation in geometry, equipping themselves to tackle a plethora of triangle-related problems with confidence.<\/p>\n<p><strong>Also Check:<\/strong><\/p>\n<ul>\n<li><strong>Class 7 Maths Exercise 6.2<\/strong><\/li>\n<li><strong>Class 7 Maths Exercise 6.3<\/strong><\/li>\n<\/ul>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/cbse\/cbse-class-7-maths-syllabus\/\"> <button class=\"btn btn-primary\" style=\"width: 100%; cursor: pointer;\" type=\"button\">CBSE Class 7 Maths Syllabus<\/button> <\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_7_Maths_Chapter_6_Exercise_65_Updated_for_2024-25\"><\/span>NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 Updated for 2024-25<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Here are the solutions for Class 7 Maths chapter 6 exercise 6.5 questions<\/p>\n<p><strong>1. PQR is a triangle, right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-73786\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-6-The-Triangle-and-its-Properties-Ex-6.5-1.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5 1\" width=\"237\" height=\"135\" \/><br \/>\n<strong>Solution:<\/strong><\/p>\n<p>In right angled triangle PQR, we have<br \/>\nQR<sup>2<\/sup> = PQ<sup>2<\/sup> + PR<sup>2<\/sup> From Pythagoras property)<br \/>\n= (10)<sup>2<\/sup> + (24)<sup>2<\/sup><br \/>\n= 100 + 576 = 676<br \/>\n\u2234 QR = \\(\\sqrt{676}\\) = 26 cm<br \/>\nThe, the required length of QR = 26 cm.<\/p>\n<p><strong>2. ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-73787\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-6-The-Triangle-and-its-Properties-Ex-6.5-2.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5 2\" width=\"249\" height=\"135\" \/><\/p>\n<p>Solution:<\/p>\n<p>In right angled\u2206ABC, we have<br \/>\nBC<sup>2<\/sup> + (7)<sup>2<\/sup> = (25)<sup>2<\/sup> (By Pythagoras property)<br \/>\n\u21d2 BC<sup>2<\/sup> + 49 = 625<br \/>\n\u21d2 BC<sup>2<\/sup> = 625 \u2013 49<br \/>\n\u21d2 BC<sup>2<\/sup> = 576<br \/>\n\u2234 BC = \\(\\sqrt{576}\\) = 24 cm<br \/>\nThus, the required length of BC = 24 cm.<\/p>\n<p><strong>3. A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-73788\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-6-The-Triangle-and-its-Properties-Ex-6.5-3.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5 3\" width=\"210\" height=\"118\" \/><\/p>\n<p>Solution:<\/p>\n<p>Here, the ladder forms a right angled triangle.<br \/>\n\u2234 a<sup>2<\/sup> + (12)<sup>2<\/sup> = (15)<sup>2<\/sup> (By Pythagoras property)<br \/>\n\u21d2 a<sup>2<\/sup>+ 144 = 225<br \/>\n\u21d2 a2 = 225 \u2013 144<br \/>\n\u21d2 a<sup>2<\/sup> = 81<br \/>\n\u2234 a = \\(\\sqrt{81}\\) = 9 m<br \/>\nThus, the distance of the foot from the ladder = 9m<\/p>\n<p><strong>4. Which of the following can be the sides of a right triangle?<\/strong><\/p>\n<ol style=\"list-style-type: lower-roman;\">\n<li><strong>2.5 cm, 6.5 cm, 6 cm.<\/strong><\/li>\n<li><strong>2 cm, 2 cm, 5 cm.<\/strong><\/li>\n<li><strong>1.5 cm, 2 cm, 2.5 cm<\/strong><\/li>\n<\/ol>\n<p>Solution:<\/p>\n<p>(i) Given sides are 2.5 cm, 6.5 cm, 6 cm.<br \/>\nSquare of the longer side = (6.5)<sup>2<\/sup> = 42.25 cm.<br \/>\nSum of the square of other two sides<br \/>\n= (2.5)<sup>2<\/sup> + (6)<sup>2<\/sup> = 6.25 + 36<br \/>\n= 42.25 cm.<br \/>\nSince, the square of the longer side in a triangle is equal to the sum of the squares of other two sides.<br \/>\n\u2234 The given sides form a right triangle.<\/p>\n<p>(ii) Given sides are 2 cm, 2 cm, 5 cm .<br \/>\nSquare of the longer side = (5)<sup>2<\/sup> = 25 cm Sum of the square of other two sides<br \/>\n= (2)<sup>2<\/sup> + (2)<sup>2<\/sup> =4 + 4 = 8 cm<br \/>\nSince 25 cm \u2260 8 cm<br \/>\n\u2234 The given sides do not form a right triangle.<\/p>\n<p>(iii) Given sides are 1.5 cm, 2 cm, 2.5 cm<br \/>\nSquare of the longer side = (2.5)<sup>2<\/sup> = 6.25 cm Sum of the square of other two sides<br \/>\n= (1.5)<sup>2<\/sup> + (2)<sup>2<\/sup> = 2.25 + 4<br \/>\nSince 6.25 cm = 6.25 cm = 6.25 cm<br \/>\nSince the square of longer side in a triangle is equal to the sum of square of other two sides.<br \/>\n\u2234 The given sides form a right triangle.<\/p>\n<p><strong>5. A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.<\/strong><\/p>\n<p>Solution:<\/p>\n<p>Let AB be the original height of the tree and broken at C touching the ground at D such that<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73789\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-6-The-Triangle-and-its-Properties-Ex-6.5-4.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5 4\" width=\"192\" height=\"174\" \/><br \/>\nAC = 5 m<br \/>\nand AD = 12 m<br \/>\nIn right triangle \u2206CAD,<br \/>\nAD<sup>2<\/sup> + AC<sup>2<\/sup> = CD<sup>2<\/sup> (By Pythagoras property)<br \/>\n\u21d2 (12)<sup>2<\/sup> + (5)<sup>2<\/sup> = CD<sup>2<\/sup><br \/>\n\u21d2 144 + 25 = CD<sup>2<\/sup><br \/>\n\u21d2 169 = CD<sup>2<\/sup><br \/>\n\u2234 CD = \\(\\sqrt{169}\\) = 13 m<br \/>\nBut CD = BC<br \/>\nAC + CB = AB<br \/>\n5 m + 13 m = AB<br \/>\n\u2234 AB = 18 m .<br \/>\nThus, the original height of the tree = 18 m.<\/p>\n<p><strong>6. Angles Q and R of a \u0394PQR are 25<sup>o<\/sup> and 65<sup>o<\/sup>.<\/strong><\/p>\n<p><strong>Write which of the following is true:<\/strong><\/p>\n<ol style=\"list-style-type: lower-roman;\">\n<li><strong>PQ<sup>2<\/sup> + QR<sup>2<\/sup> = RP<sup>2<\/sup><\/strong><\/li>\n<li><strong>PQ<sup>2<\/sup> + RP<sup>2<\/sup> = QR<sup>2<\/sup><\/strong><\/li>\n<li><strong>RP<sup>2<\/sup> + QR<sup>2<\/sup> = PQ<sup>2<\/sup><\/strong><\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-73790\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-6-The-Triangle-and-its-Properties-Ex-6.5-5.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5 5\" width=\"221\" height=\"115\" \/><br \/>\nSolution:<br \/>\nWe know that<br \/>\n\u2220P + \u2220Q + \u2220R = 180\u00b0 (Angle sum property)<br \/>\n\u2220P + 25\u00b0 + 65\u00b0 = 180\u00b0<br \/>\n\u2220P + 90\u00b0 = 180\u00b0<br \/>\n\u2220P = 180\u00b0 \u2013 90\u00b0 \u2013 90\u00b0<br \/>\n\u2206PQR is a right triangle, right angled at P<\/p>\n<p>(i) Not True<br \/>\n\u2234 PQ<sup>2<\/sup> + QR<sup>2<\/sup> \u2260 RP<sup>2<\/sup> (By Pythagoras property)<\/p>\n<p>(ii) True<br \/>\n\u2234 PQ<sup>2<\/sup> + RP<sup>2<\/sup> = QP<sup>2<\/sup> (By Pythagoras property)<\/p>\n<p>(iii) Not True<br \/>\n\u2234 RP<sup>2<\/sup> + QR<sup>2<\/sup> \u2260 PQ<sup>2<\/sup> (By Pythagoras property)<\/p>\n<p><strong>7. Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-73791\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-6-The-Triangle-and-its-Properties-Ex-6.5-6.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5 6\" width=\"171\" height=\"131\" \/><br \/>\nSolution:<\/p>\n<p>Given: Length AB = 40 cm<br \/>\nDiagonal AC = 41 cm<br \/>\nIn right triangle ABC, we have<br \/>\nAB<sup>2<\/sup> + BC<sup>2<\/sup>= AC<sup>2<\/sup> (By Pythagoras property)<br \/>\n\u21d2 (40)<sup>2<\/sup> + BC<sup>2<\/sup> = (41)<sup>2<\/sup><br \/>\n\u21d2 1600 + BC<sup>2<\/sup> = 1681<br \/>\n\u21d2 BC<sup>2<\/sup> = 1681 \u2013 1600<br \/>\n\u21d2 BC<sup>2<\/sup> = 81<br \/>\n\u2234 BC = \\(\\sqrt{81}\\) = 9 cm<br \/>\n\u2234 AB = DC = 40 cm and BC = AD = 9 cm (Property of rectangle)<br \/>\n\u2234 The required perimeter<br \/>\n= AB + BC + CD + DA<br \/>\n= (40 + 9 + 40 + 9) cm<br \/>\n= 98 cm<\/p>\n<p><strong>8. The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-73792\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-6-The-Triangle-and-its-Properties-Ex-6.5-7.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5 7\" width=\"195\" height=\"216\" \/><\/p>\n<p>Solution:<\/p>\n<p>Let ABCD be a rhombus whose diagonals intersect each other at O such that AC = 16 cm and BD = 30 cm<br \/>\nSince, the diagonals of a rhombus bisect each other at 90\u00b0.<br \/>\n\u2234 OA = OC = 8 cm and OB = OD = 15 cm<br \/>\nIn right \u2206OAB,<br \/>\nAB<sup>2<\/sup> = OA<sup>2<\/sup> + OB<sup>2<\/sup> (By Pythagoras property)<br \/>\n= (8)<sup>2<\/sup>+ (15)<sup>2<\/sup> = 64 + 225<br \/>\n= 289<br \/>\n\u2234 AB =\\(\\sqrt{289}\\)= 17 cm<br \/>\nSince AB = BC = CD = DA (Property of rhombus)<br \/>\n\u2234 Required perimeter of rhombus<br \/>\n= 4 \u00d7 side = 4 \u00d7 17 = 68 cm.<\/p>\n<p><button><strong>NCERT Solutions for Class 7 Maths Chapter-wise PDF<\/strong><\/button><\/p>\n<ul>\n<li><strong>Chapter 1 <\/strong><strong>Integers<\/strong><\/li>\n<li><strong>Chapter 2 Fractions and Decimals<\/strong><\/li>\n<li><strong>Chapter 3 Data Handling<\/strong><\/li>\n<li><strong>Chapter 4 Simple Equations<\/strong><\/li>\n<li><strong>Chapter 5 Lines and Angles<\/strong><\/li>\n<li><strong>Chapter 6 The Triangles and Its Properties<\/strong><\/li>\n<li><strong>Chapter 7 Congruence of Triangles<\/strong><\/li>\n<li><strong>Chapter 8 Comparing Quantities<\/strong><\/li>\n<li><strong>Chapter 9 Rational Numbers<\/strong><\/li>\n<li><strong>Chapter 10 Practical Geometry<\/strong><\/li>\n<li><strong>Chapter 11 Perimeter and Area<\/strong><\/li>\n<li><strong>Chapter 12 Algebraic Expressions<\/strong><\/li>\n<li><strong>Chapter 13 Exponents and Powers<\/strong><\/li>\n<li><strong>Chapter 14 Symmetry<\/strong><\/li>\n<li><strong>Chapter 15 Visualizing Solid Shapes<\/strong><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_7_Maths_Chapter_6_Exercise_65_PDF_Download\"><\/span>NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 PDF Download<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download the NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 in PDF format to ensure comprehensive preparation and a deeper understanding of the concepts. These expertly crafted solutions help students tackle various mathematical problems with ease, enhancing their ability to score higher in exams. Click here to access and download the PDF now for detailed, step-by-step solutions that support your study efforts efficiently. Get your free copy today and excel in your Maths exams.<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" style=\"width: 66.4777%; height: 168px;\" cellspacing=\"0\" cellpadding=\"4\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td style=\"text-align: center; width: 108.127%; height: 24px;\" colspan=\"2\" align=\"left\"><b>Other Resources for Class 7<\/b><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 44.3422%; height: 24px;\" align=\"left\"><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-7\/\"><strong>NCERT Exemplar Solutions Class 7<\/strong><\/a><\/td>\n<td style=\"width: 63.7748%; text-align: left; height: 24px;\" align=\"right\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-books\/class-7\">NCERT Books for Class 7<\/a><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 44.3422%; height: 24px;\" align=\"left\"><a href=\"https:\/\/infinitylearn.com\/surge\/worksheet-class-7\/\"><strong>Class 7 Worksheets<\/strong><\/a><\/td>\n<td style=\"width: 63.7748%; text-align: left; height: 24px;\" align=\"right\"><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-7\/\"><strong>NCERT Solutions for Class 7<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_NCERT_Solutions_for_Class_7_Maths_Chapter_6_Exercise_65\"><\/span>FAQs on NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_Pythagoras_theorem_in_Chapter_6_The_Triangle_and_its_Properties_of_Exercise_65_in_NCERT_Class_7_Maths\"><\/span>What is Pythagoras&#039; theorem in Chapter 6 The Triangle and its Properties of Exercise 6.5 in NCERT Class 7 Maths?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn Chapter 6, The Triangle and its Properties, of Exercise 6.5 in NCERT Class 7 Maths, Pythagoras' theorem is described as stating that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_will_the_final_exams_benefit_from_using_the_NCERT_Solutions_for_Class_7_Maths_Chapter_6_The_Triangle_and_its_Properties_Exercise_65\"><\/span>How will the final exams benefit from using the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5)?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tUsing the NCERT Solutions for Class 7 Maths Chapter 6, The Triangle and its Properties (Exercise 6.5), offers several benefits for final exam preparation. These solutions provide clearly solved examples and step-by-step methods to solve problems, enhancing students' understanding of key concepts and equipping them with strategies to tackle complex questions in the final exams.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_a_Rhombus_in_Class_7_Maths_Chapter_6_The_Triangle_and_its_Properties\"><\/span>What is a Rhombus in Class 7 Maths Chapter 6 The Triangle and its Properties?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn Class 7 Maths, Chapter 6 The Triangle and its Properties, a rhombus is defined as a type of parallelogram characterized by four sides of equal length, opposite sides that are parallel, and opposite angles that are equal. Additionally, the diagonals of a rhombus bisect each other at right angles.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_a_Rectangle_in_Class_7_Maths_Chapter_6_The_Triangle_and_its_Properties\"><\/span>What is a Rectangle in Class 7 Maths Chapter 6 The Triangle and its Properties?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA rectangle, as described in Class 7 Maths, Chapter 6 The Triangle and its Properties, is a type of quadrilateral with four right angles, making it a parallelogram where each angle is a right angle and all angles are equal. A special case of a rectangle is a square, where all four sides are of equal length.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Where_can_I_find_the_most_up-to-date_NCERT_Solutions_for_Class_7_Maths_Chapter_6_The_Triangle_and_its_Properties_Exercise_65\"><\/span>Where can I find the most up-to-date NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5)?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe latest NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5) can be found on Infinity Learn, India\u2019s premier e-learning platform. These solutions are meticulously crafted by subject experts at Infinity Learn, adhering to CBSE guidelines, ensuring clarity and precision in the material.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is Pythagoras' theorem in Chapter 6 The Triangle and its Properties of Exercise 6.5 in NCERT Class 7 Maths?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In Chapter 6, The Triangle and its Properties, of Exercise 6.5 in NCERT Class 7 Maths, Pythagoras' theorem is described as stating that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How will the final exams benefit from using the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5)?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Using the NCERT Solutions for Class 7 Maths Chapter 6, The Triangle and its Properties (Exercise 6.5), offers several benefits for final exam preparation. These solutions provide clearly solved examples and step-by-step methods to solve problems, enhancing students' understanding of key concepts and equipping them with strategies to tackle complex questions in the final exams.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is a Rhombus in Class 7 Maths Chapter 6 The Triangle and its Properties?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In Class 7 Maths, Chapter 6 The Triangle and its Properties, a rhombus is defined as a type of parallelogram characterized by four sides of equal length, opposite sides that are parallel, and opposite angles that are equal. Additionally, the diagonals of a rhombus bisect each other at right angles.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is a Rectangle in Class 7 Maths Chapter 6 The Triangle and its Properties?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A rectangle, as described in Class 7 Maths, Chapter 6 The Triangle and its Properties, is a type of quadrilateral with four right angles, making it a parallelogram where each angle is a right angle and all angles are equal. A special case of a rectangle is a square, where all four sides are of equal length.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Where can I find the most up-to-date NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5)?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The latest NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties (Exercise 6.5) can be found on Infinity Learn, India\u2019s premier e-learning platform. These solutions are meticulously crafted by subject experts at Infinity Learn, adhering to CBSE guidelines, ensuring clarity and precision in the material.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Class 7 Maths Chapter 6 Exercise 6.5 Solution &#8211; Triangle and Its Properties The NCERT solutions for Class 7 Maths [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"ncert solutions for class 7 maths chapter 6 exercise 6.5","_yoast_wpseo_title":"NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 PDF for 2024-25","_yoast_wpseo_metadesc":"Download pdf of NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 -Triangle and its Properties for the year 2024-25 form Infinity 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