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
8 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