SOLUTION: Aleah's garden borders a wall. She buys 80 meters of fencing. What dimensions maximize the area of the garden.

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Question 1021424: Aleah's garden borders a wall. She buys 80 meters of fencing. What dimensions maximize the area of the garden.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
There are three borders using the fencing.
2L%2BW=80
The area is then,
A=L%2AW
Substituting from the perimeter,
A=L%2880-2L%29
It's a quadratic, convert to vertex form.
A%28L%29=80L-2L%5E2
A%28L%29=-2L%5E2%2B80L
A%28L%29=-2%28L%5E2-40L%29
A%28L%29=-2%28L%5E2-40L%2B400%29%2B2%2A400
A%28L%29=-2%28L-20%29%5E2%2B800
So the maximum occurs when L=20m and the value is A%2820%29=800m%5E2
Then,
20%2AW=800
W=40m