From a rectangle ABCD of area 768 sqcm, a semicircular part with diameter AB and area 72π sqcm is removed. The perimeter of the leftover portion, in cm, is:
Explanation:
The area of the semicircle = 72π sq. cm. If ‘r’ is the radius of the semi-circular portion removed,
We get π×r22=72
Therefore r = 12 cm. Therefore the diameter of the semi-circle = AB = 24 cm.
Area of rectangle ABCD = 768 sq. cm.
Therefore the length of side AC =76824=32 cm.
The perimeter of the leftover portion
= Perimeter of the semicircle + l(AD) + l(DC) + l(CB) = 12π + 32 + 24 + 32 = 88 + 12π
Hence, option (a).
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