SOLUTION: A rectangular field is to be made along a river. if one side is to have the river as a natural boundary, what are the dimensions of the largest rectangular field that can be enclos

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Question 343917: A rectangular field is to be made along a river. if one side is to have the river as a natural boundary, what are the dimensions of the largest rectangular field that can be enclosed by using 240 meters of fence for the other 3 sides?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For this rectangle,
P=2W%2BL=240
The L side is parallel to the river.
The area of this rectangle is,
A=L%2AW
From the perimeter equation,
L=240-2W
Substitute in the area equation,
A=%28240-2W%29W
A=240W-2W%5E2
Convert the area equation to vertex form, y=a%28x-h%29%5E2%2Bk.
The function has a maximum at the vertex (h,k).
Complete the square to convert to vertex form.
A=-2W%5E2%2B240W
A=-2%28W%5E2-120W%29
A=-2%28W%5E2-120W%2B3600%29%2B2%283600%29
A=-2%28W-60%29%5E2%2B7200
The maximum area of 7200 sq.m. occurs when W=60m.
L=240-2%2860%29
L=240-120
L=120m
The rectangular field if 60m x 120m.