Question

If the area of three circles are in ratio $4:9:25$ what is the ratio of their radii.

Answer 1

Solve for the ratio of the radii of the circles.

Given that area of three circles are in the ratio $4:9:25$

Let the radii of the three circles be $a,b$ and $c$

We know that the formula for the area of the circle is $A={\mathrm{\pi r}}^2$

$\Rightarrow r\propto \sqrt{A}$

We need to find the ratio of their radii hence will take the square root of the areas of the circle

So ratio of radii of circles $=\sqrt{4}:\sqrt{9}:\sqrt{25}=2:3:5$

Hence the radii are in the ratio of $2:3:5$