SOLUTION: A farmer has 3000 feet of wire to enclose a rectangular field. He plans to fence the entire area and hen subdivide it by running a fence across the middle. Find the dimensions of

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Question 810649: A farmer has 3000 feet of wire to enclose a rectangular field. He plans to fence the entire area and hen subdivide it by running a fence across the middle. Find the dimensions of the field that would enclose the maximum area . What is the maximum area?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Rectangle dimensions would be like, x and y. One more term of either x or y occurs as the divider fence length. You are not clear about running this subdividor accross the middle. Diagonally, or perpendicularly?

I am choosing the diagonal, because now no need to look at choice of either x or y. The total fence length using variables would be 2x%2B2y%2Bdiagonal=3000.

That diagonal is x%5E2%2By%5E2=d%5E2
d=sqrt%28x%5E2%2By%5E2%29

So fencing length is 2x%2B2y%2Bsqrt%28x%5E2%2By%5E2%29=3000 and the area is xy=A

Solve the fence length equation for either x or y.
sqrt(x^2+y^2)=3000-2x-2y
x^2+y^2=(3000-2(x+y))^2
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Excuse me. This is easier to do on paper than in text form typed into a website page.

The plan is solve the fencing equation for either x or y, substitute this into the Area equation or function, and then find the derivative; and set equal to zero and solve for the variable. Then calculate the other variable.