Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(a) 2 units
(b) n units
(c) 4 units
(d) 7 units

Given: 

Area and perimeter of a circle are numerically equal.

To do: 

We have 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 numerically equal.

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

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

$\Rightarrow r^2=2r$

$\Rightarrow r=2$ unit

Therefore, the radius of the circle is $2$ units.

Option A is the correct answer.

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Updated on: 10-Oct-2022

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