SOLUTION: A petting zoo is working to construct a rectangular pen. The pen will have 2 partitions to create separate spaces for goats,sheep,and pigs. The petting zoo has 1000 feet of fencing

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Question 1085512: A petting zoo is working to construct a rectangular pen. The pen will have 2 partitions to create separate spaces for goats,sheep,and pigs. The petting zoo has 1000 feet of fencing to use.
a. Write an area function (A(x)) that gives the area of the enclosure as a function of the length of a partition, x.
b. Find the dimensions of the pen that will provide the greatest area.
c. What is the maximum area that can be enclosed?
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = the length of a partition
= the total length of the 2 partitions
plus the ends that are parallel to the 2 partitions
= the length of the other side of the pen

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(a)

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(b)
This is a parabola with a maximum. Use the formula:

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Now find
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The dimensions for maximum area are:
125 x 250
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(c)

31,250 ft2
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check the answer:

OK