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# 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 the rectangle so that its area is maximum.find also the area

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hi

$\\let the side on the diameter makes an angle \theta with the line joining center to one of the vertices of rectangle \\=>l=2rcos\theta \\=>b=rsin\theta \\=>a=lb=r^2sin2\theta \\=>{da \over d\theta}=r^2*2(cos2\theta)=0 \\=>cos2\theta=0 \\=>2\theta={\pi \over 2} \\=>\theta = {\pi \over 4}$

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty