Question

What is the radius of a circle whose area is equal to the sum of the areas of two circles whose radii are $5$ metres and $12$ metres.

Answer 1

If $r$ be the radius of the required circle,
then $\pi r^2=\pi 5^2+\pi {12}^2$
$\Rightarrow r^2=25+144=169$
$\Rightarrow r=13$