Question 785587
An architect wants to design a window with an area of 24 square feet in the shape of a rectangle with a semicircle on top. If x is the width of the window, express the perimeter P of the window as a function of x. 
:
Find the area of the semicircle: 
a = {{{.5*pi*(.5x)^2}}}
a = {{{.5*pi*.25x^2}}}
Find the circumference of the semi circle
C = {{{.5*pi*x}}}
:
The area of the rectangular portion:
A = 24 - {{{.5*pi*.25x^2}}}
:
The length of the rectangle is the area divided by the width which is x
L =  {{{((24 - (.5*pi*.25x^2)))/x}}}
:
Perimeter = 2L + x + semicircle circumference
P(x) = {{{(2(24 - (.5*pi*.25x^2)))/x}}} + x + {{{.5*pi*x}}}