SOLUTION: A farmer has 1200 m of fence to enclose a pasture for his cows. The pasture will border a river. The pasture is to be the shape of a right trapezoid with the length of its paralle

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Question 1098923: A farmer has 1200 m of fence to enclose a pasture for his cows. The pasture will border a river. The pasture is to be the shape of a right trapezoid with the length of its parallel sides in the ratio 1:2. The angled side of the pasture is to be on the river so it does not need fence. What is the maximum area that the farmer can enclose? Show the steps of your solution.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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A=XY%2B%281%2F2%29%28XY%29=%283%2F2%29XY
and
2X%2BY%2BX=1200
3X%2BY=1200
Y=1200-3X
Substituting to get the area as a function of only one variable,
A=%283%2F2%29X%281200-3X%29
A=%283%2F2%29%28-3X%5E2%2B1200X%29
Complete the square to get the area to vertex form,
A=-%289%2F2%29%28X%5E2-400X%29
A=-%289%2F2%29%28X%5E2-400X%2B200%5E2%29%2B%289%2F2%29%28200%5E2%29
A=-%289%2F2%29%28X-200%29%5E2%2B%289%29%28200%2A100%29
A=-%289%2F2%29%28X-200%29%5E2%2B180000
Vertex solution is the maximum.
A%5Bmax%5D=180000m%5E2 when X=200m