Two posts, one 13 feet high and the other 27 feet high, stand 32 feet apart. They are to be stayed by two guy wires, attached to a single stake, running from ground level to the top of each post. Where should the stake be placed to use the least wire? The function that expresses the length of the wire in terms of the distance the stake is from the 13 foot post is $\displaystyle {W}{\left({x}\right)}=\sqrt{{{x}^{{2}}+{13}^{{2}}}}+\sqrt{{{\left({32}-{x}\right)}^{{2}}+{27}^{{2}}}}$.



What are reasonable values to use for $\displaystyle {x}$? (What is the domain in context of the problem.)

Find the value of $\displaystyle {x}$, which uses the least amount of wire. Select an answer ft^2 ft^3 ft

How much wire will be used? Select an answer ft ft^3 ft^2