Question

If the ratio of the areas of two squares is 9 : 1, then the ratio of their perimeters is

(a) 2 : 1 (b) 3 : 1 (c) 3 : 2 (d) 4 : 1

Answer 1

Let a and b be the sides of the squares, then as per the question
$\frac{a^2}{b^2}=\frac{9}{1}\Rightarrow {\left(\frac{a}{b}\right)}^2=\frac{3^2}{1}\Rightarrow \frac{a}{b}=\frac{3}{1}$
Therefore
$\mathrm{Ratio}\mathrm{of}\mathrm{the}\mathrm{perimeters}\mathrm{of}\mathrm{the}\mathrm{squares}=\frac{4a}{4b}=\frac{a}{b}=\frac{3}{1}$
Thus, the of the required ratio is 3 : 1.
Hence, the correct option is (b).