Question

If the perimeter of two similar triangles is in the ratio 2 : 3, what is the ratio of their sides?

Options

• 4 : 9

• 2 : 3

• `sqrt(2)` : `sqrt(3)`

• 3 : 2

Answer 1

2 : 3

Explanation:

Let two similar triangles be ABC and DEF.

Since, the triangles are similar,

∴ `("Perimeter" (ΔABC))/("Perimeter" (ΔDEF)) = (AB)/(DE)`

According to the question,

 `("Perimeter" (ΔABC))/("Perimeter" (ΔDEF)) = 2/3`

∴ `(AB)/(DE) = 2/3`

Thus, the ratio of sides is 2 : 3.