SOLUTION: Marlon wants to fence a rectangular area that has one side bordered by an irrigation. If he has 80 m of fencing materials, what are the dimensions and the maximum area he can enclo

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Marlon wants to fence a rectangular area that has one side bordered by an irrigation. If he has 80 m of fencing materials, what are the dimensions and the maximum area he can enclo      Log On


   

Question 1097035: Marlon wants to fence a rectangular area that has one side bordered by an irrigation. If he has 80 m of fencing materials, what are the dimensions and the maximum area he can enclose?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length along be irrigation side by Y and the width be X.
The fence would then have a perimeter of P=2X%2BY=80
The area enclosed would be A=XY
From the perimeter equation,
Y=80-2X
Substituting into the area equation,
A=X%2880-2X%29=-2X%5E2%2B80X
To find the maximum area, convert to vertex form,
A%28X%29=-2%28X%5E2-40X%29
A%28X%29=-2%28X%5E2-40X%2B400%29%2B800
A%28X%29=-2%28X-20%29%5E2%2B800
So the maximum area of 800m%5E2 occurs when X=20m,
So then,
Y=80-2%2820%29
Y=80-40
Y=40m