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The perimeter of the square is equal to the perimeter of the semicircle. The sum of the perimeter of semicircle and square is 72 cm, then, what is the ratio of the area of the semicircle and the area of the square?

The perimeter of the square is equal to the perimeter of the semicircle. The sum of the perimeter of semicircle and square is 72 cm, then, what is the ratio of the area of the semicircle and the area of the square? Correct Answer 77 : 81

Given:

The perimeter of square = Perimeter of a semicircle

The perimeter of square + Perimeter of semicircle = 72 cm

Formula used:

The perimeter of square = 4 × side

Perimeter of semicircle = πr + 2r

Area of square = side × side

Area of semicircle = πr2/2

Calculation:

The sum of the perimeter of circle and square is 72 cm

Suppose the side of the square = x cm

Radius of semicircle = r cm

⇒ 4x = (πr + 2r)

⇒ 4x = (22r/7 + 2r)

⇒ 4x = 36r/7

⇒ x = 9r/7

So, 4x + (πr + 2r) = 72

⇒ 4x + 36r/7 = 72

⇒ 36r/7 + 36r/7 = 72

⇒ r = 7 cm

And, x = 9 cm

So, Area of the square (9 × 9) = 81 sq. cm

Area of semicircle = π(7× 7)/2

⇒ 77

∴ required ratio = 77 : 81

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