find the dimensions of the rectangle of the greatest area that can inscribeD in a semicircle of radius r?? NOTE: NOT MENTIONED THAT ONE OF THE SIDE IS ON DIAMETER Share with your friends Share 0 Garima Singhal answered this Let ABCD be the rectangle of length 2x and breadth y that is inscribed in a semicircle of radius r and centre O.Join OC.Let ∠BOC = θNow, x = r cos θ; y = r sin θArea of rectangle = length × breadthA = 2x × yA = r2 sin 2θdAdθ = 2r2 cos 2θFor maxima or minima,dAdθ = 0⇒2r2 cos 2θ = 0⇒cos 2θ = cos π2⇒θ = π4Now, d2Adθ2 = -4r2 sin 2θ⇒d2Adθ2θ=π/4 = -4r2 < 0So, area is maximum at θ = π4Now, length = 2x = 2r cos π4 = 2rbreadth = y = r sin θ = r sin π4 = r2 = 2r2 1 View Full Answer