Question: A piece of wire of length L cm is cut into two pieces. One piece, of length x cm, is made into a circle; the rest is made into a square.
(a) Find the value of x that makes the sum of the areas of the circle and square a minimum. Find the value of x giving a maximum.
(b) For the values of x found in part (a), show that the ratio of the length of wire in the square to the length of wire in the circle is equal to the ratio of the area of the square to the area of the circle.3
(c) Are the values of x found in part (a) the only values of x for which the ratios in part (b) are equal?