# Ex.12.1 Q5 Areas Related to Circles Solution - NCERT Maths Class 10

## Question

Tick the correct answer in the following and justify your choice: If the perimeter and the 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

## Text Solution

**What is known?**

Perimeter and area of the circle are numerically equal.

**What is unknown?**

Radius of circle.

**Reasoning:**

Given that Perimeter and area of the circle are numerically equal. We get \(2\pi \rm{r}= \pi \rm{r^2}.\)

Using this relation we find the radius.

**Steps:**

Let the radius of the circle \(= r.\)

Circumference of circle \( = 2\pi r\)

Area of circle \(= \pi \rm{r^2}\)

Given that, the circumference of the circle and the area of the circle are equal.

This implies \[\begin{align}2\pi \rm{r} &= \pi \rm{r^2}\\2 &= \rm{r}\end{align}\]

Therefore, the radius of the circle is \(2\) units.

Hence, the correct answer is \(\rm{A.}\)