Maximum area of a rectangle and semi-circle

A window is made up of two shapes-- a rectangle and a semicircle. (semicircle is attached to top of rectangle). If the perimeter of the entire window is 16 ft, what would the length and width of the rectangle need to be in order to maximize the amount of light shining through the window?

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Originally Posted by Chica513

A window is made up of two shapes-- a rectangle and a semicircle. (semicircle is attached to top of rectangle). If the perimeter of the entire window is 16 ft, what would the length and width of the rectangle need to be in order to maximize the amount of light shining through the window?

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The window is known as a 'norman window'. If you search MHF using these two key words, or in fact use Google, you will find many examples of this exact type of question.