Problem 4.

A Norman window has the shape of a rectangle surmounted by a semicircle whose diameter is the same as the length of the bottom side of the rectangle. If the perimeter of a Norman window is to be 20 feet what should the length of the bottom side be in order for the window to let in the most light; that is, what should the length of the bottom side be in order to maximize the area of the window? Please leave in your answer (do not use a decimal or fractional estimate for ), and please simplify your answer as much as possible.




[Problem submitted by Vin Lee, LACC Associate Professor of Mathematics. Source: Precalculus, 5th ed. by Michael Sullivan, Prentice Hall, 1999.]