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A Norman window consists of rectangle surmounted by a semicircle.
If the perimeter of a Norman window is 20 ft, what should be the radius of the semicircle
and the height of the rectangle such that the window will admit most light?
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Let x = width and diameter;
y = height of the rectangle part.
Then the perimeter
P = ====> + = 20 ====> y = .
The area A = + = + =
= - - + = + -
Then the condition for the maximum area = 0 takes the form
= 0, or = 10 ====> x = = = 5.60 ft.
The maximum area is when the radius of the semicircle is 5.60/2 = 2.80 ft and the height of the rectangular part is
y = = = 2.804 ft.
Solved.