Solution: Given that the perimeter and area of the circle are numerically equal. Let's assume a circle of radius 'r'. Circumference of the circle = 2πr Area of circle = πr2 The circumference of the circle and the area of the circle are equal. Thus, we have 2πr = πr2 2 = r Therefore, the radius of the circle is 2 units. Hence, the correct answer is A. ☛ Check: NCERT Solutions for Class 10 Maths Chapter 12 Video Solution: NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 5 Summary: The radius of the circle is 2 units if the perimeter and the area of a circle are numerically equal. ☛ Related Questions: Math worksheets and We have given that circumference and area of a circle are numerically equal. Let it be x. Let r be the radius of the circle, therefore, circumference of the circle is `2pi r^2`and area of the circle will bepir^2. Therefore, from the given condition we have, `2pir=x...............(1)` `pir^2=x.............(2)` Therefore, from equation (1)get r=x/2x. Now we will substitute this value in equation (2) we get , `pi (x/2pi)^2=x` Simplifying further we get, `pi xx x^2/(4pi^2)=x` Cancelling x we get, `pixx x^2/(4pi^2)=x` Now we will cancel` pi` `x/4pi=1`...........(3) Therefore, area of the circle is `4pi sq.unit` |