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    

                          .