Question
The perimeter of a sector of a circle, whose radius is
18 cm, is 62 cm. If the length of a rectangle is 10 cm more than the arc subtended by the sector and its perimeter is 96 cm, then find the area (in cm2) of the rectangle.Solution
Let the arc subtended by the sector be âlâ cm and the radius of the circle be ârâ cm According to the question, (l + 2r) = 62 Or, l = 62 â 2r = 62 â (2 Ă 18) = 26 cm Therefore, length of the rectangle = 26 + 10 = 36 cm Let the breadth of the rectangle be âbâ cm Therefore, 2 Ă (36 + b) = 96 Or, b = 48 â 36 = 12 cm Therefore, area of the rectangle = length Ă breadth = 12 Ă 36 = 432 cm2
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