SOLUTION: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 400 feet of fencing to fence off the other three sides.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 400 feet of fencing to fence off the other three sides.       Log On


   

Question 1077442: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 400 feet of fencing to fence off the other three sides. What dimensions should the lot I have if the enclosed area is to be a maximum?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, distance from highway to side opposite of the highway
y, distance of the side parallel to but opposite of the highway

Fence length to use, 2x%2By=400

Area to hold, xy

Area, A%28x%29=x%28400-2x%29
Parabola shape and equation A%28x%29=x%28400-2x%29, with vertex as the maximum point.

x%28400-2x%29=0 gives the roots
x%28200-x%29=0
system%28Roots%2Cx=0%2Cand%2Cx=200%29

Maximum A will be at x=100, exactly in the middle of the roots.

2x%2By=400
y=400-2x
y=400-2%2A100
y=400-200
y=200


Dimensions for maximum area:
100 and 200
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Two sides 100 and one side 200.