Question

The perimeters of two similar triangles are 15cm and 24cm respectively . Find the ratio of their respective areas

Answer 1

Linear scale factor = 15/24 = 5/8

Area scale factor = (Linear scale factor)² = (5/8)² = 25/64

∴ The ratio of their respective areas = 25 : 64

Answer 2

Solution :-

We know that the ratio of 2 similar triangles is equal to the ratio of their corresponding sides.

So, 

Perimeter of the 1st Δ/Perimeter of the 2nd Δ = Side of the 1st Δ/Side of the 2nd Δ

⇒ 15/24 = Side of the 1st Δ/Side of the 2nd Δ

⇒ Side of the 1st Δ/Side of the 2nd Δ = 5/8

Also, we know that the ratio of areas of 2 similar triangles is equal to the squares of the ratio of their corresponding sides.

So, 

Area of 1st Δ/Area of 2nd Δ = (Side of 1st Δ/Side of 2nd Δ)²

⇒ (5/8)²

= 25/64

= 25 : 64

So, the ratio of their respective areas is 25 : 64

Answer.