If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is

(a) 225 : 256
(b) 256 : 225
(c) 15 : 16
(d) 16 : 15

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Solution

(c) 15 : 16

Let the two squares be ABCD and PQRS.

Further, let the lengths of each side of ABCD and PQRS be x and y, respectively.

Therefore

$\frac{A r e a o f s q . A B C D}{A r e a o f s q . P Q R S}$ = $\frac{x^{2}}{y^{2}}$

⇒ $\frac{x^{2}}{y^{2}}$ = $\frac{225}{256}$

Taking square roots on both sides, we get:

$\frac{x}{y}$ = $\frac{15}{16}$

Now, the ratio of their perimeters:

$\frac{P e r i m e t e r o f s q . A B C D}{P r i m e t e r o f s q . P Q R S}$ = $\frac{4 \times s i d e o f s q . A B C D}{4 \times S i d e o f s q . P Q R S}$ = $\frac{4 x}{4 y}$

⇒ $\frac{P e r i m e t e r o f s q . A B C D}{P r i m e t e r o f s q . P Q R S}$ = $\frac{x}{y}$

⇒ $\frac{P e r i m e t e r o f s q . A B C D}{P r i m e t e r o f s q . P Q R S}$ = $\frac{15}{16}$

Thus, the ratio of their perimeters = 15 : 16

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