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 .