Anorman 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.) x = ft

Answer-

For x = 2.24, greatest possible amount of light will be admitted.

Solution-

According to the question, the perimeter of the window is 16 ft

From the attachment,

Perimeter of the window = Perimeter of the rectangle-Width of the rectangle + Curved perimeter of the semi-circle

So,

As we have to find the value of x so that the greatest possible amount of light is admitted, so we have to calculate the maximum area for which the perimeter is 16 ft.

So,

Putting the value of y in terms of x,

Now, equating the first derivative of A to 0,

Therefore, for x= 2.24, greatest possible amount of light will be admitted.