Problem 2

A Norman window is in the shape of a half circle on top of a rectangle. Suppose the vertical side of the rectangular part of a certain Norman window is r feet (r>0), the radius of the circular part is also r feet, the perimeter of the window is p feet, and the area of the window is p square feet. What are the radius and perimeter of the window? Write your answers in simplest form.

[Problem submitted by Vin Lee, LACC Associate Professor of Mathematics.]

Solution for Problem 2:

Since perimeter = area, .

So, r = 2.

And

.