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A rectangle is inscribed in a semi-circl...

A rectangle is inscribed in a semi-circle of radius `r` with one of its sides on diameter of semi-circle. Find the dimensions of rectangle so that the area is maximum. Find the area also.

Text Solution

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`A(theta)=widthxxheight`
`=(2rcostheta)xxrsintheta`
`=2r^2sinthetacostheta`
`=r2xx(2sinthetacostheta)`
`=sin2theta`
`A(theta)=x^2xxsin(2theta)`
`sin(2theta)=1`
`2theta=pi/4`
...
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