Question 68092
A rancher plans to use 160 yards of fencing to enclose a rectangular corral and to divide it into two parts by a fence parallel to the shorter sides of the corral. Find the dimensions of the corral if its area is 100 yd^2.
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As written this problem does not make sense, that much fence would have a
much larger area. I'm going to assume you meant 1000 sq yds
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Perimeter in this case would be
2L + 3W = 160
2L = 160 - 3W
L = 160/2 - (3/2)W
L = 80 - 1.5W
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The area:
L*W = 1000
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Substitute (80-1.5W) for L in the area equation:
(80-1.5W) * W = 1000
:
80W - 1.5W^2 = 1000
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Arrange as a quadratic equation:
-1.5W^2 + 80W - 1000 = 0
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Using the quadratic formula, solutions are W=20 and W=35 which make sense:
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Using a width of 20 yds would make the length: 80 - 1.5(20) = 50 yds
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This checks out: 2(50) + 3(20) = 160