Question

Ratio of areas of two similar triangles is 9 : 25. _______ is the ratio of their corresponding sides.

Options

• 3 : 4

• 3 : 5

• 5 : 3

• 25 : 81

Answer 1

3 : 5

Explanation:

Let ΔABC and ΔPQR be two similar triangles.  

According to the given condition,

`(A(ΔABC))/(A(ΔPQR)) = 9/25`   ...(Given)

But `(A(ΔABC))/(A(ΔPQR)) = (AB^2)/(PQ^2)`   ...(By the theorem of areas of similar triangles)

∴ `(AB^2)/(PQ^2) = 9/25`

∴ `(AB)/(PQ) = 3/5`

∴ 3 : 5 is the ratio of their corresponding sides.