Question

Q. The areas of two similar triangles are 25 cm2 and 36 cm2 respectively. If the perimeter of the second triangle is 24 cm, find the corresponding perimeter of the first triangle.
(The answer is supposed to be 2cm; please include the working.)

Answer 1

Answer:

area ratio = (side)² ratio

25:36 = (S1)² :(S2)²

so,

(S1):(S2) = 5:6 = Perimeter ratio .

Given ,

6--------------24

5--------------20 (Ans.)

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Answer 2

Answer:

20 cm

Step-by-step explanation:

The areas of two similar triangles are 25 sq.cm and 36 sq.cm respectively.

We are given that the perimeter of the second triangle is 24 cm,

Let the perimeter of first triangle be x

Theorem : the ratio of the area of the similar triangles is equal to the ratio of the square of their corresponding triangles

So, $\frac{25}{36}=\frac{x^2}{24^2}$

$\frac{25 \times 24^2}{36}=x^2$

$\sqrt{\frac{25 \times 24^2}{36}}=x$

$20 cm=x$

Hence  the corresponding perimeter of the first triangle is 20 cm