A norman window has the shape of the rectangle surmounted by a semicircle.
Observe the figure.
be the radius of the semicircle.
and are the length and width of the rectangle.
Therefore the perimeter of the norman window is .
But perimeter of the window is ft.
The area of the window is the area of rectangle and area of semicircle.
Therefore the area of the window is .
Apply derivative on each side with respect to .
The area of the rectangle is maximum when its first derivative becomes zero.
Equate to zero.
Therefore the radius of the semicircle is .
Substitute in .
Therefore the length of the rectangle is .
Therefore the width of the rectangle is .
The radius of the semicircle is .
The length of the rectangle is .
The width of the rectangle is .
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