SOLUTION: A rectangular part of a parking lot is to be fenced off to allow some repairs to be done. The workers have fourteen 3-m sections of pre-assembled fencing to use. They want to cr

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Question 1067969: A rectangular part of a parking lot is to be fenced off to allow some repairs to be done.
The workers have fourteen 3-m sections of pre-assembled fencing to use.
They want to create the greatest possible area in which to work.
a) How can the fencing be used to create as large an enclosed area as possible?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let X be the number of width sections they use and Y be the number of height sections they use,
X%2BY=14
And the area that they create is,
A=XY
A=X%2814-X%29
A=14X-X%5E2
Complete the square to get the area in vertex form to find the greatest area,
A=-%28X%5E2-14X%2B49%29%2B49
A=-%28X-7%29%5E2%2B49
So the maximum area of 49 units occurs when X=7
Then,
7%2BY=14
Y=7
and each unit has 9 sq meters (3x3).
So,
A%5Bmax%5D=49%2A9
A%5Bmax%5D=441m%5E2
and the shape is a square with a side length of 21m.