Question

Find the ratio of the perimeter for the pair of similar two regular pentagons with areas 144 in² and 36 in²

Answer 1

The ratio between the perimeter of the largest and smallest pentagon is 2.

How to find the ratio between the perimeters?

We know that the pentagons are similar, meaning that the dimensions of one of the pentagons is k times the dimensions of the other.

Because of this, the ratio between the areas is k squared. And because the perimeter depends linearly on the dimensions, the ratio between the perimeters will be equal to k.

So we need to find k, we will have:

$\frac{144 in^2}{36 in^2} = k^2 = 4\\\\k = \sqrt{4} = 2$

Then we conclude that the ratio between the perimeters is k  =2.

If you want to learn more about similar shapes:

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