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# A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle. See Exercise 1.1.62.) If the perimeter of the window is $30 ft$, find the dimensions of the window so that the greatest possible amount of light is admitted.

## Maximum Light is admitted through the window, When :Radius of the semi-circular part is $\frac{30}{4+\pi} \approx 4.2 f t$Dimensions of the rectangular part of the window are 8.4$f t \times 4.2 f t$

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