SOLUTION: A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. It has 80 feet of fencing that is to be used to fence off the other three

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. It has 80 feet of fencing that is to be used to fence off the other three      Log On


   

Question 1115738:
A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. It has 80 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?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Dimensions x and y;
2x%2By=80
-
A=xy

A%28x%29=x%2880-2x%29


x%2880-2x%29=0
x%2840-x%29=0
-
system%28Roots_Are%2C0%2Cand%2C40%29

The maximum for A occurs exactly between the two roots, so maximum A is at highlight_green%28x=20%29. This means highlight_green%28y=40%29.

This max area A=20%2A40=highlight%28800%29.