Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is:

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Perimeter = 2 r + r θ = 20 θ = 20 - 2 r r Now, Area A = r 2 θ 2 ⇒ A = r 2 2 20 - 2 r r = 10 r - r 2 ⇒ d A d r = 10 - 2 r = 0 ⇒ r = 5 d 2 A d r 2 r = 5 = - 2 < 0 ⇒ r = 5 is the point of maxima A m a x = 10 × 5 - 25 = 25

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