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

⇒ πr² = 2π × r

⇒ r² = 2r 

⇒ r² - 2r =0

⇒ r(r - 2) = 0

⇒ r - 2 = 0     [∴ r ≠ 0]

⇒ r = 2 units 

Hence, the radius of the circle is 2 units.