Question
The perimeter of a sector of a circle, whose radius is
17 cm, is 63 cm. If the length of a rectangle is 10 cm more than the arc subtended by the sector and its perimeter is 98 cm, then find the area (in cm2) of the rectangle.Solution
Let the arc subtended by the sector be βlβ cm and the radius of the circle be βrβ cm According to the question, (l + 2r) = 63 Or, l = 63 β 2r = 63 β (2 Γ 17) = 29 cm Therefore, length of the rectangle = 29 + 10 = 39 cm Let the breadth of the rectangle be βbβ cm Therefore, 2 Γ (39 + b) = 98 Or, b = 49 β 39 = 10 cm Therefore, area of the rectangle = length Γ breadth = 10 Γ 39 = 390 cm2
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