SOLUTION: A rancher plans to use 160 yd 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
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Question 245071: A rancher plans to use 160 yd 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 1000yds squared.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A rancher plans to use 160 yd 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 1000yds squared.
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Draw the picture.
Let the shorter side of the rectangle be "x".
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3 shorter sides = 3x yrds
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Each of the longer sides is (160-3x)/2
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Area = shorter * longer
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1000 = x
1000 = 80x - (3/2)x^2
2000 = 160x - 3x^2
3x^2 -160x + 2000 = 0
x = [160 +- sqrt(160^2 - 4*3*2000)]/6
x = [160 +- sqrt(1600)]/6
Positive solution:
x = [160 + 40]/6
x = 200/6
x = 33 1/3 yrds. (side)
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(160-3(100/3))/2 = 30 yrds. (other side)
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Cheers,
Stan H.
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