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Question
A farmer is constructing three equally-sized pens against the side of a barn for his animals, as shown in the image below. He has 108 feet of fence to construct the pens, No fence is needed along the barn. What is the maximum possible area for one of the pens? You may enter an exact answer or round your answer to the nearest hundredth.

Provide your answer below:
\[
\text { Maximum area }=\square \mathrm{ft}^{2}
\]
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Step 1 ：The problem is asking for the maximum possible area for one of the pens. The farmer has 108 feet of fence and is constructing three equally-sized pens against the side of a barn. Since no fence is needed along the barn, the total length of the fence will be divided into four parts: three for the sides of the pens parallel to the barn and one for the sides of the pens perpendicular to the barn.

Step 2 ：Therefore, each side of the pen parallel to the barn will be \( \frac{108}{4} = 27 \) feet.

Step 3 ：The area of a rectangle is given by the formula length * width. In this case, the length is the side of the pen parallel to the barn and the width is the side of the pen perpendicular to the barn. Since the pens are squares (as they are equally-sized), the length and the width are equal.

Step 4 ：Therefore, the maximum possible area for one of the pens is \( 27 * 27 = 729 \) square feet.

Step 5 ：Final Answer: The maximum possible area for one of the pens is \( \boxed{729} \) square feet.