Question 55

The ratio of the areas of two squares is 16 : 1. Find the ratio between their perimeters.

Solution

Let the length of side of two squares be $$a$$, $$b$$ respectively

Given, ratio of areas of two squares = 16:1

$$=$$> $$\frac{a^2}{b^2}=\frac{16}{1}$$

$$=$$> $$\left(\frac{a}{b}\right)^2=\frac{16}{1}$$

$$=$$> $$\frac{a}{b}=\frac{4}{1}$$

$$=$$> $$\frac{4a}{4b}=\frac{4}{1}$$

$$\therefore\ $$Ratio of their perimeters = 4:1

Hence, the correct answer is Option A

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