SOLUTION: You have a 500 foot roll of fencing, which is to form three sides of a rectangular enclosure (the fourth side is an existing brick wall). What are the dimensions of the enclosure w

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Question 330225: You have a 500 foot roll of fencing, which is to form three sides of a rectangular enclosure (the fourth side is an existing brick wall). What are the dimensions of the enclosure with the maximum area?
Any help would really be appreciated!!!!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.P=W%2BL%2BW=2W%2BL=500
2.A=LW
From eq. 1,
L=500-2W
Substitute into eq. 2,
A=%28500-2W%29W=500W-2W%5E2
To find the maximum value of A, convert the equation to vertex form,
A%28W%29=a%28W-h%29%5E2%2Bk where (h,k) is the vertex.
THe value of k is the maximum value for the function A(x).
500W-2W%5E2=-2%28W%5E2-250W%29
A%28W%29=-2%28W%5E2-250W%2B15625%29%2B2%2815625%29
A%28W%29=-2%28W-125%29%5E2%2B31250
So the maximum area of 31250 ft^2 occurs when W=125.
From eq. 1,
250%2BL=500
L=250
The rectangle has the dimension of 125 ft wide by 250 ft long.