Question 213554
A farmer wants to make a rectangular enclosure along the side of a barn and then divide the enclosure into two pens with a fence constructed at a right angle to the barn. If 300 yards of fencing are available, what are the dimensions of the largest section that can be enclosed? 
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_________________Barn
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I think it looks something like this:
Then we can write an equation for the 300 yds of fencing
L + 3W = 300
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L = (300-3W)
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Area = L*W
Replace L with (300-3W)
A = (300-3W) * W
Arrange as a quadratic equation
A = -3W^2 + 300W
Find the axis of symmetry for Width that gives max area x = -b/(2a)
in this equation a=-3; b=300 
W = -300/(2*-3)
W = -300/-6
W = +50 ft is the width for max area
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Find the length
L = 300 - 3(50)
L = 150 ft is the length
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Max area would be 150 * 50 = 7500 sq/ft