ADVANCED EXERCISES

(1) A Norman window has the shape of a rectangle with a semicircle on top. If the perimeter of the window is 30 m, express the area A of the window as a function of the width x of the window.

Let x = width of window
    l = length of window

    Perimeter = 30 = 2l + x + (x/2)
                ==> 2l = 30 - (2 + )x/2
                     l = 15 - (2 + )x/4

            (x/2)2 
    Area =  ------- + Lx
              2

         = x2/4         (2 + )x2
           ----- + 15x - ---------
              2              4

         = x2          (2 + )x2
           ---- + 15x - ----------
             8            4

         = -4 - 
           ------- x2 + 15x
              8

The area of the window expresses in terms of x is given by:
            -4 - 
            ------- x2 + 15x
               8