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 `2pir`and area of the circle will be `pir^2`. Therefore, from the given condition we have, `2pir=x .................(1)` `pi r^2 = x ...............(2)` Therefore, from equation (1) get `r=x/(2pi)`. Now we will substitute this value in equation we get, `pi(x/(2pi))^2=x` Simplifying further we get, `pixx x^2/(4pi^2)=x` Cancelling x we get, `pi xx x/(4pi^2)=1` Now we will cancel `pi` `x/(4pi)=1...........(3)` Now we will multiply both sides of the equation (3) by `4pi` we get, `x=4pi` We can rewrite this equation as given below, `x=2xxpixx2` Comparing equation (4) with equation (1) we get r = 2. Therefore, radius of the circle is 2. We know that diameter of the circle is twice the radius of the circle. `∴ "diameter"=2xx "radius"` `∴ "diameter"=2xx2` `∴"diameter"=4` Therefore, diameter of the circle is 4. Hence, option (d) is correct.
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