# Tick the correct answer in the following and justify your choice.

Question:

Tick the correct answer in the following and justify your choice. If the perimeter and area of a circle are numerically equal, then the radius of the circle is

(A) 2 units

(B) $\pi$ units

(C) 4 units

(D) 7 units

Solution:

(A) We have

[Numerical area of the circle]

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

$\Rightarrow \pi r^{2}-2 \pi r=0$

$\Rightarrow r^{2}-2 r=0$

$\Rightarrow \mathrm{r}(\mathrm{r}-2)=0$

$\Rightarrow \mathrm{r}=0$ or $\mathrm{r}=2$

But r cannot be zero

$\therefore \mathrm{r}=2$ units.

Thus, the radius of circle is 2 units.