State whether the given statement is True or False.

Statement: It is possible to construct a triangle of sides 5 cm, 6cm and 7cm and then a triangle similar to it whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

Question

State whether the given statement is True or False.

Statement: It is possible to construct a triangle of sides 5 cm, 6cm and 7cm and then a triangle similar to it whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

Accepted Answer

Let us first draw the triangle with sides 5 cm, 6cm and 7cm.
- Firstly, draw line AB of length 5cm which will be the base of the triangle.
- Now with the help of a compass, we will draw an arc of 6cm from the point A.
- Similarly, we will draw an arc of 7cm from point B.
- Finally, we will mark the point of intersection of two arcs from A and B as C and then draw the lines joining the points A and C and A and B.

https://www.vedantu.com/question-sets/2a0c9576-ed85-4729-b93c-7136f97295804943682573035560644.png

Now we will construct a similar triangle of ABC whose sides are

\frac{7}{5}

of the corresponding sides of ΔABC.
Firstly, we will draw a line AY which makes an acute angle with line AB on the opposite side of vertex C.

https://www.vedantu.com/question-sets/55716267-8848-4671-845e-02151d824f378268545128778495042.png

Now we will mark seven points (as 7 is greater than 5 in the fraction

\frac{7}{5}

) at equal distances from each other on the line AY i.e. AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7

https://www.vedantu.com/question-sets/633eedf1-0e40-47d5-b6ee-4c33826ee39e3084541855372665460.png

Now we will draw a line joining A5 to B and then we will draw a line A7 B′ parallel to A5 B and intersect the line AB at B′.
.

https://www.vedantu.com/question-sets/dd5989b8-acba-469c-b457-5988e58762bd4299202784032350143.png

Then we draw a line from B′ to extended AC such that it intersects AC at C′ and the line B′C′ is parallel to the line BC.

https://www.vedantu.com/question-sets/583f62ca-0aae-4ea3-8805-19b04c8465051901879896824030155.png

Now we can see the new triangle i.e. ΔAB′C′ is the similar triangle to ΔABC.
Hence, It is possible to construct a triangle of sides 5 cm, 6cm and 7cm and then a triangle similar to it whose sides are