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Question

The maximum area of a rectangle that can be inscribed in a circle x2+y2=25 is equal to (in sq units)

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Solution

Let l,b be the length and breadth of
the rectangle, here r=5
we have l2+b2=100(i)
Area of rectangle, A=lb
Let f=A2=l2b2=l2(100l2)
f=200l4l3
f=20012l2
f=0l=50(l0)
f(50)<0
f is maximum when l=50
b=50
Hence maximum area =50 sq units

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