Question

The ratio of corresponding sides of similar triangles is 3 : 5; then find the ratio of their areas.

Answer 1

Let the ratio of corresponding sides of similar triangles be S₁ and S₂, and A₁ and A₂ be their corresponding areas.

Given: The two triangles are similar. 

S₁ : S₂ = 3 : 5

∴ `("S"_1)/("S"_2) = 3/5`   ...(i)

By the Theorem of areas of similar triangles,

`("A"_1)/("A"_2) = ("S"_1)^2/("S"_2)^2`

`("A"_1)/("A"_2) = (("S"_1)/("S"_2))^2`

`("A"_1)/("A"_2) = (3/5)^2`   ...[From (i)]

`("A"_1)/("A"_2) = 9/25`

∴ The ratio of areas of similar triangles = 9 : 25.