The side parallel to the highway be x ft
let each of the other two sides by y
2x + y = 640
y = 640 - 2x
area = xy = x(640-2x)
= -2x^2 + 640x
I assume you know how to find the vertex of this downwards parabola, and that vertex is
(160 , 51200)
if x = 160
y = 640 - 2(160) = 320
the lot should be 320 ft by 160 ft
Houston Community College is planning to construct a rectangular parking lot on land
bordered on one side by a highway. The plan is to use 640 ft of fencing to fence off the
other three sides. What should the dimensions of the lot be if the enclosed area is to be a
maximum?
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