SOLUTION: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. it has 800 FEET of fencing that is to be used to fence off the other three s

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Question 1140793: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. it has 800 FEET of fencing that is to be used to fence off the other three sides. what should be the dimensions of the lot if the enclosed area is to be a maximum? what is the maximum area?
PLEASE HELP this question is on my test for math lab and i’ve been stuck for an hour now trying to do it!!!! it would mean the world to me if someone helped me!!!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A college is planning to construct a rectangular parking lot on land bordered on one side by a highway.
it has 800 FEET of fencing that is to be used to fence off the other three sides.
what should be the dimensions of the lot if the enclosed area is to be a maximum? what is the maximum area?
:
let L = the length of the parking lot
let w = the width
:
Three sides are fenced, therefore
L + 2w = 800
L = -2w+800
:
the area
A = L*w
replace L with
A = w(-2w+800)
A = -w^2 + 800w
this is a quadratic equation, max area is on the axis of symmetry x = -b/2a
w = %28-800%29%2F2%28-2%29
w = + 200 ft is the width for max area
Find the length
L = -2(200) + 800
L = 400 ft is length
:
Find the max area: 200*400 = 80,000 sq/ft