Posted by **Z32** on Monday, June 22, 2009 at 12:59am.

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 22 feet?

- Calculus -
**drwls**, Monday, June 22, 2009 at 6:17am
Write equations for:

(1) area of the window in terms of the semicircle diameter (x) and height (y) of the rectangle.

(2) Perimeter = constant = 22 ft

A = (pi/2)*x^2 + x*y= (pi +1)x + 2y

P = (pi+1)x + 2y = 22

Eliminate the variable y by making the substitution

y = 11 - [(pi+1)/2]x into the first equation for (A), making it an equation in one variable, x.

Solve dA/dx = 0 for the optimum x.

- Calculus -
**Anonymous**, Monday, March 30, 2015 at 11:05pm
34.288

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