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.