A Norman window has the shape of a semicircle atop a rectangle

Question

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 35 feet? 

Answer 1

The solution is just messy, but straight forward.

Let h be the height of the rectangular part of the window.

Then d+2h+(1/2)πd = 35

and A=dh+(1/2)π(d/2)²

Use the 1st equation to express h as a function of d.

Substitute this expression for h in the area equation.

Differentiate A with respect to d and set the derivative=0 and solve for d.

This gives you the needed dimensions.