Find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing?

1 Answer
Dec 2, 2017

Total rectangle = 42.9 xx 85.8
Area = 3680

Explanation:

First, the "maximum" area is irrelevant - it can only be the product of the sides, which is the same for any rectangular perimeter.

In this case it is really just two identical rectangles with a shared side. SO, if we call them "X x Y" rectangles, the overall fence used is 3X + 4Y = 300. The area of the combined space is X xx 2Y, which is the same area for any constant sum of X and Y.

Because the relative values do not affect the area, we can take a square as a reasonable geometry for the individual sections. In that case, X = Y, so the overall fence use is 3X + 4X = 300
X = 300/7 = 42.9 = Y
The total area is X xx 2Y = 42.9 xx 42.9 xx 2 = 3680
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