If the perimeter and the area of a circle are numerically equal, then find the radius of the circle.

Given: Area and perimeter of a circle are numerally equal.

To do: To find the radius of the circle.

Solution:

Let $r$ be the radius of the circle.

$\therefore$ Area of the circle$=\pi r^2$

Perimeter of the circle $=2\pi r$

As given, area and perimeter of the circle are numerally equal.

$\Rightarrow \pi r^2=2\pi r$

$\Rightarrow r^2=\frac{2\pi r}{\pi}$

$\Rightarrow r^2=2r$

$\Rightarrow r=2$ unit

Thus, the radius of the circle is $2$ unit.

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Updated on: 10-Oct-2022

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