Hello, G-Rex!

Imagine a fenced-in area composed of a rectangle with one side being a semicircle.

The perimeter of this fence is 498 feet.

Maximize the area of this pen. Code:

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| r r |
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x | | x
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2r

The radius of the semicircle is

Hence, the length of the rectangle is

Let the width of the rectangle be

The semicircle has perimeter

The rectangular portion of the pen has perimeter

We have: .

The area of the semicircle is: .

The area of the rectangle is: .

The area of the pen is: .

Substitute [1] into [2]: .

. . which simplifies to: .

And that is the function we must maximize . . .