the agriculture club needs to fence off rectangular area at the state fair to separate the sheep , p

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the agriculture club needs to fence off rectangular area at the state fair to separate the sheep , pigs,goats and chicken they need to fence a large rectangular area and then divide it into four smaller equal size pens for each type of animal , they have 600 feet of fencing available. what is the maximum area that can be fenced

Oct 14th, 2015

Hello!

Denote one side of the outer rectangle as x and the second as y. We need three sides of each length (for outer and inner sides).

So 3(x+y)=600, or x+y=200, or y=200-x.

The area is xy=x(200-x)=-x^2+200x. It is a parabola branches down, it has a maximum at -200/(-2)=100.

The area will be 100*100=10,000(square feet).

Please ask if something is unclear.
Oct 14th, 2015

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Oct 14th, 2015
Sep 26th, 2017
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