SOLUTION: How do you find the area for this expression?: Erik has 2000 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. W

Question 916913: How do you find the area for this expression?: Erik has 2000 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do you find the area for this expression?: Erik has 2000 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
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Perimeter = 2(length + width)
2000 = 2(length + width)
length + width = 1000
L = 1000-W
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Area = Length*Width
A = (1000-W)*W
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Area = 1000W-W^2
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Maximum Area occurs when W = -b/(2a) = -1000(2*-1) = 500
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If Width = 500, Length = 1000 - 500 = 500
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Ans: Area = 500^2 = 250000 sq. units
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Cheers,
Stan H.
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