Calculus

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 20 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
My base length is correct: (10/1+pi/4)
But I need the total height, thanks so much!!

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  1. do you mean
    base = 2 r = 10/(1+pi/4) ??
    if that is correct then

    2r + 2h + pi r = 20

    total height = h + r

    10/(1+pi/4) + 2 h + pi(5/(1+pi/4) = 20

    10 + 2h(1+pi/4) +5 pi = 20

    2h(1+pi/4) = 10-5pi

    h = (10-5pi)/(2+pi/2)
    then to get total height add r
    r+h = 5/(1+pi/4) + (5-2.5pi)/(1+pi/4)
    = (10-2.5 pi) /(1+pi/4)

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  2. It is showing up as incorrect :(

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