Question

The breadth of a rectangle is equal to the radius of a circle, the ratio of areas of circle and rectangle is 33 ∶ 16. Then the length of rectangle is what percentage greater the breadth of the rectangle?

1. 105.8%
2. 152.4%
3. 52.4%
4. 50.8%
5. 48.5%

Answer 1

Correct Answer - Option 3 : 52.4%

Radius of circle(r) = Breadth of rectangle(b)

The ratio of areas of circle and rectangle is 33 ∶ 16

⇒ (π × r²)/(l × b) = 33/16

l → length of rectangle

⇒ (π × b²)/lb = 33/16

⇒ 22b/7l = 33/16

⇒ l/b = 32/21

∴ Let l = 32x and b = 21x

∴ Required percentage = {(32x – 21x)/21x} × 100 = 52.38% ≈ 52.4%  

∴ The length of rectangle is 52.4% greater the breadth of the rectangle