Assume you have 12 yards of fencing material available What is the largest area, measured in square yards, of a rectangular enclosure that has a fenced center divider (so that the final enclosure looks like a domino from above)

The maximum area is when the largest side of the rectangle is 3 yards and the shortest side of the rectangle is 2 yards.

Step-by-step explanation:

If the final enclosure will look froma above like a domino (rectangular with a center divider).

If we name a and b the sides of the rectangle, we have the area as:

If we divide the center of the rectangle with a size b fence (one of the sides of the rectangle), the perimeter used is:

To maximize the area, we derive and equal to zero (after replacement of a by the last equation):

The maximum area is when the largest side of the rectangle is 3 yards and the shortest side of the rectangle is 2 yards.

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