Question 1099343: A rancher plans to use 200 yards of fencing to enclose a rectangular corral and to divide it into two parts with a fence parallel to the shorter sides of the corral. Find the dimensions of the corral if its area is to be 1600 square yards.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the corral will essentially have 3 widths, 2 ends and the one in the middle dividing it. There are two lengths.
the width=x, and there are 3 of them
what is left over is 200-3x, and that is 2 lengths, so that one length is half that or 100-(3/2)x
The area is their product, x(100-1.5x)=-1.5x^2+100x, and that equals 1600
-1.5x^2+100x-1600=0
1.5x^2-100x+1600=0
3x^2-200x+3200=0
x=(1/6)(200+/- sqrt (200^2-12(3200)), and sqrt term is 40000-38400=1600, and that is 40
the roots are (1/6)(240)=40 yds width, and the length is 100-60=40 yds as well. The width is 40 yds, length is 40 yds and area is 1600 yds^2,
also (1/6)160=26 2/3 yds width. The length is 100-40=60 yds, so the corral is 60*26 (2/3)=1600 yds^2.
40 x 40
60 x 26 2/3
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