SOLUTION: A farmer has 200 yards of fencing to enclose three sides of a rectangular piece of property that lies next to a river. The river will serve as the fourth side. Find the dimensions

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Question 987860: A farmer has 200 yards of fencing to enclose three sides of a rectangular piece of property that lies next to a river. The river will serve as the fourth side. Find the dimensions of property if the area is 3200 yards^2. (There will be 2 solutions)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
You can choose the sides as x, x, and y, and then the fencing length is 2x+y=200 and xy=3200 for area. This gives the system of equations

system%282x%2By=200%2Cxy=3200%29.

y=200-2x
;
x%28200-2x%29=3200
-2x%5E2%2B200x=3200
-2x%5E2%2B200x-3200=0
2x%5E2-200x%2B3200=0
highlight%28x%5E2-100x%2B1600=0%29

Discriminant, 10000-4%2A1600=10000-6400=3600=60%5E2;

highlight%28x=%28100%2B-+60%29%2F2%29


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x=20 and y=160, or x=80 and y=40
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