Chapter 6.1, Problem 51E

EXERCISES

Area A piece of wire $12$ ft long is cut into two pieces. (See the figure.) One piece is made into circle and other piece is made into square. Let the piece of length $x$ can be formed into a circle. We allow $x$ to equal $0$ or $12,$ so all the wire may be used for the square for the circle.

Radius of circle = $\frac{x}{2\pi }$	Area of circle = ${\left(\frac{x}{2\pi }\right)}^2$
Side of square = $\frac{12-x}{4}$	Area of square = ${\left(\frac{12-x}{4}\right)}^2$

Where should the cut be made in order to minimize the sum of the areas enclosed by both figures?