If the perimeter of the window is 16ft, find the value of x so that the greatest possible amount ... ?

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.) If the perimeter of the window is 16 ft, find the value of x so that the greatest possible amount of light is admitted. (Give your answer correct to two decimal places.)