[size=13Hello, pseizure2000![/size]

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 45 feet? Code:

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2r

The radius of the semicircle is

Then the width of the rectangle is

Let = height of the rectangle.

The perimeter is: . . **[1]**

The area of the window is: . . **[2]**

Substitute [1] into [2]: .

. . which simplifies to: . . **[3]**

Differentiate and equate to zero: .

. . Hence: .

Substitute into [3]: .

. . and we get: .