Question

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

Answer 1

Let the corresponding sides of similar triangles be s₁ and s₂.

Let A₁ and A₂ be their corresponding areas.

s₁ : s₂ = 3 : 5 ......[Given]

∴ `s_1/s_2 = 3/5` ......(i)

`A_1/A_2 = (s_1^2)/(s_2^2)` .......[Theorem of areas of similar triangles]

= `((s_1)/(s_2))^2`

= `(3/5)^2`  ......[From (i)]

= `9/25`

∴ Ratio of areas of similar triangles = 9 : 25