Joey wants to build a rectangular garden. he plans to use a side of a river for one side of the garden, so he will not place fencing along this side of the garden. he has 92 yards of fencing material. what is the maximum area that will be enclosed? enter your answer in the box.

Let the shorter side of the rectangle be x and the longer side be y. The perimeter of the rectangle, excluding the side next to the river, will be equal to the total length of fence Joey has. Therefore:
2x + y = 92
y = 92 - 2x

Moreover, the area of the rectangle will be:
Area = xy

Substituting y,
Area = x(92 - 2x)
92x - 2x² = Area

Now, if we differentiate the area with respect to x and equate it to 0, we can find the length that will give us the maximum area.
92 - 4x = 0
x = 23 yards

Therefore, the shorter side should be 23 yards and the longer side should be 46 yards and the total area enclosed will be:
23 * 46 = 1058 square yards

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