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harkovskaia [24]
3 years ago
12

A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of th

e sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?

Enter your answer in the box.


ft²

Mathematics
1 answer:
Katarina [22]3 years ago
5 0
Let x represent the length of the side of the pen that is parallel to the barn. Then the area (y) will be
.. y = x(300 -x)/2
This describes a downward opening parabola with zeros at x=0 and x=300. The vertex (maximum) will be found at the value of x that is halfway between those, x = 150.

For that value of x, the pen area is
.. y = 150(300 -150)/2 = 150^2/2 = 11,250 . . . . . square feet.

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