Question

If the perimeter and thearea of a circle are numerically equal, then the radius of the circle is
a. 2 units
b. units
c. 4 units
d 7 unit​

Answer 1

Given : Perimeter and area of circle are numerically equal

To find : Radius of circle

Formula used :

• Area of circle = π r²
• Perimeter of circle = circumference = 2πr

Steps to follow :

• As we are given that area = perimeter, we will equate formula of perimeter and area
• And then will be solving the equation for radius

Solution :

Area = Perimeter

$\sf \implies \: \pi( {r}^{2} ) = 2\pi \: r \\ \\ \sf \implies \: {r}^{2} = \frac{2\pi}{\pi} \times r \\ \\ \sf \implies \: \frac{ r \times r }{r} = 2 \\ \\ \sf \implies \bold{r \: = \: 2}$

ANSWER : Option a) 2 units