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Area of circle is equal to the area of a rectangle having perimeter of 144 cms and length more than the breadth by 16 cms. What is the radius of the circle?
1. 7cms
2. 35cms
3. 14cms
4. 28cms
5. None of these

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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.

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