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

(b) 3:1

Let a side of the first square be a cm and that of the second square be b cm.
Then, their areas will be a² and b², respectively.
Their perimeters will be 4a and 4b, respectively.

According to the question:
$\frac{a^2}{b^2}=\frac{9}{1}$⇒ ${\left(\frac{a}{b}\right)}^2=\frac{9}{1}={\left(\frac{3}{1}\right)}^2$⇒ $\frac{a}{b}=\frac{3}{1}$

∴ Required ratio of the perimeters = $\frac{4a}{4b}=\frac{4\times 3}{4\times 1}=\frac{3}{1}$= 3:1