SOLUTION: 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

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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.
The only part I could figure out is that the radius is (x/2)?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Api%2A%28.5x%29%5E2
a = .5%2Api%2A.25x%5E2
Find the circumference of the semi circle
C = .5%2Api%2Ax
:
The area of the rectangular portion:
A = 24 - .5%2Api%2A.25x%5E2
:
The length of the rectangle is the area divided by the width which is x
L = %28%2824+-+%28.5%2Api%2A.25x%5E2%29%29%29%2Fx
:
Perimeter = 2L + x + semicircle circumference
P(x) = %282%2824+-+%28.5%2Api%2A.25x%5E2%29%29%29%2Fx + x + .5%2Api%2Ax