SOLUTION: what are the dimensions of the largest rectangular field that can be enclosed wi5h 60 meters of wire

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Question 959210: what are the dimensions of the largest rectangular field that can be enclosed wi5h 60 meters of wire
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the rectangle is,
A=L%2AW
The perimeter of the rectangle is fixed at,
P=2L%2B2W=60
L%2BW=30
L=30-W
Substituting into the area,
A=%2830-W%29W
A=30W-W%5E2
Now the area is the function of only one variable.
We can convert to vertex form to find the maximum value.
A=-W%5E2%2B30W
A=-%28W%5E2-30W%2B225%29%2B225
A=-%28W-15%29%5E2%2B225
So when W=15m the maximum area of 225m%5E2 is achieved.
L=30-15
L=15m
So the rectangle that gives the max area is a square of side 15m.