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

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

Solution:

Let the radius of the required circle be r.
Now, Area of circle = Perimeter of the circle

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

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

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

$\Rightarrow r(r-2)=0$

$\Rightarrow r-2=0 \quad[\because r \neq 0]$

$\Rightarrow r=2$ units

Hence, the radius of the circle is 2 units.

 

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