SOLUTION: 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 dimensi

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Question 68092This question is from textbook Algebra and Trigonometry
: 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 are is 100yd2. This question is from textbook Algebra and Trigonometry

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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.
:
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
:
Perimeter in this case would be
2L + 3W = 160
2L = 160 - 3W
L = 160/2 - (3/2)W
L = 80 - 1.5W
:
The area:
L*W = 1000
:
Substitute (80-1.5W) for L in the area equation:
(80-1.5W) * W = 1000
:
80W - 1.5W^2 = 1000
:
Arrange as a quadratic equation:
-1.5W^2 + 80W - 1000 = 0
:
Using the quadratic formula, solutions are W=20 and W=35 which make sense:
:
Using a width of 20 yds would make the length: 80 - 1.5(20) = 50 yds
:
This checks out: 2(50) + 3(20) = 160