question_answer 82)

Show that of al the rectangles inscribed in a given fixed circle, the square has the maximum area. 

Answer:

Let x × y be the rectangle inscribed in the circle of diameter d                                ?(1)       Now Area of the rectangle ABCD       = A = xy             Let Z = A2            [Using (1)]       = d2x2 ? x4                               Now              or zero of the rectangle is maximum when x       (1)                            Hence the rectangle of maximum area is the square.