question_answer 98)

The sum of the perimeter of a circle and square is k, where k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. 

Answer:

Let r be the radius of circle and x be the side of square.       Given : combined perimeter of circle and square = k                                       ?. (1)        Combined area (A) of circle and square + x2                                                                             (by (1))                                                             [(by(1))]             Now             Hence combined area is minimum when side of square is double the radius of the circle.