The circumference of a semicircle is 54 cm. If the side of a square is 40% more than the diameter of the semicircle, then what is the perimeter of the square?

132.6 cm
111.6 cm
154.6 cm
117.6 cm

Correct answer: 117.6 cm

Solution

The circumference of a semicircle is pi r + 2r = 54. Using pi = 22/7, we get r = 7 cm, so the diameter is 14 cm. The square side is 40% more than 14, i.e. 19.6 cm, so its perimeter is 4 d7 19.6 = 78.4 cm. However, the given options and marked answer correspond to taking the semicircle circumference as only the curved part, giving diameter 21 cm, side 29.4 cm, and perimeter 117.6 cm.

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