Question

Find the radius of a circle whose perimeter and area are numerically equal.

Answer 1

Let the radius of the required circle be r.
Now, Area of circle = Perimeter of the circle
$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^2=2\mathrm{\pi }\times r \\ \Rightarrow r^2=2r \\ \Rightarrow r^2-2r=0 \\ \Rightarrow r\left(r-2\right)=0 \\ \Rightarrow r-2=0\left[\because r\ne 0\right] \\ \Rightarrow r=2\mathrm{units} \end{gathered}$$
Hence, the radius of the circle is 2 units.