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Question
The perimeter of a sector of the circle of area 25π sq.cm is 20 cm. Find the area of sector.
Solution
Area of circle = πr2
But area is given to be 25π sq.cm.
∴ 25π = πr2
∴ r2 = 25
∴ r = 5 cm
Perimeter of sector = 2r + S
But perimeter is given to be 20 cm.
∴ 20 = 2(5) + S
∴ 20 = 10 + S
∴ S = 10 cm
Area of sector = `1/2 xx "r" xx "S"`
= `1/2 xx 5 xx 10`
= 25 sq. cm.
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