Question

The ratio of the areas of similar polygons is 64: 16. What is the ratio of their sides

Answer 1

8:4

Explanation:

Given that,

The ratio of the areas of similar polygons is 64: 16, A₁:A₂=64: 16

We need to find the ratio of their sides. For similar polygons, the ratio of the area is proportional to the square of the ratio of their corresponding sides.

Let sides are x₁ and x₂. So,

`(A_1)/(A_2)=((x_1)/(x_2))^2\\\\(x_1)/(x_2)=\sqrt{(A_1)/(A_2)} \\\\=\sqrt{(64)/(16)}\\\\=(8)/(4)`

So, the required ratio is 8:4.