Question

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

• A. $225:256$
• B. $256:225$
• C. $15:16$
• D. $16:15$

Answer 1

Answer: (C)

$15:16$

Let the sides of the two squares be $x$ and $y$ respectively. Then,
Reqd. ratio of areas

$\frac{x^2}{y^2}=\frac{225}{256}\Rightarrow \frac{x^2}{y^2}=\frac{{15}^2}{{16}^2}\Rightarrow \frac{x}{y}=\frac{15}{16}$

Ratio of perimeter

$=4x:4y=\frac{4x}{4y}=\frac{x}{y}$
$=15:16$