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The maximum area possible using 100 feet of Fencing is that inside a circular fence. But, since you asked about a rectangular fence:

a 25x25 fence would hold 625 square feet.

a 10x40 fence would hold 400 square feet.

a 5x45 fence would hold 225 square feet.

As you can see, the square is the rectangle that encompasses the largest area, as it is closest to a circle.

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Q: How much maximum area can 100 ft of fence hold in a rectangle?
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