Correct Answer - Option 5 : None of these
Given:
The area of the circle is equal to the area of a rectangle
The perimeter of a rectangle is 144 cm.
The length of the rectangle more than the breadth by 16 cm.
Formula Used:
Area of circle = πr2, where r is the radius of the circle.
Perimeter of Rectangle = 2(l + b)
Area of rectangle = l × b
Here l = length, b = breadth
Calculation:
Let length of the rectangle be L cm and breadth be B cm.
So, Area of rectangle = L × B
According to the question length is more than the breadth by 16cms.
So, L = B + 16
As we know,
The perimeter of rectangle = 2 (length + breadth) = 2 (L + B)
So, 2(L + B) = 144
⇒ L + B = 72
⇒ B + 16 + B = 72
⇒ B = 28
Then, L = 28 + 16 = 44, B = 28
Hence, Area of rectangle = 44 × 28 = 1232 cm2
⇒ 1232 = πr2
⇒ r2 = (1232/π)
⇒ r = √(1232/π) = 14√2 cm
∴ Radius (r) = 14√2 cm
∴ The radius of circle is 14√2 cm.