Give a brief history of the mathematician Pythagoras. Verify Pythagoras theorem by paper cutting, folding and pasting.

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answer is D.

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Detailed Solution

Step 1: We will take a paper and draw a right angled triangle ABC right angled at C of sides 3 cm , 4 cm and 5 cm respectively. We will then cut out the triangle.
Step 2: We will paste the cut out of the triangle on a new sheet of paper.
Step 3: we will draw a square on each of the sides of triangle ABC and name them accordingly as shown in the figure below.
Step 4: We will extend FB and GA of the square GFBA so that they meet ED at P and CI at R Step 5: we will then draw a perpendicular PQ on BP
Step 6: Now, we will name the parts of the triangles formed in the square EDCB and ACIH as 1, 2, 3, 4, and 5 respectively.
Step 7: Now, we will cut out the numbered pieces. We will then place all these pieces of triangles on the square ABFG.
Area of square ACIH = (AC)2 = (3cm)2 = 9 cm2.
Also, area of square EDCB = (BC)2 = (4 cm)2 = 16 cm2 And area of square ABFG = (AB)2 = (5 cm)2 = 25 cm2 Thus, we get,
(AB)2 = (BC)2 + (AC)2 ⇒ 25 = 9 + 16 ⇒ 25 = 25
So, as LHS = RHS, it is proved.
Therefore, Pythagoras theorem is proved.

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