SOLUTION: A gardener has 270 feet of fencing and wants to fence in a rectangular garden and then divide it into two plots with a piece of fencing parallel to one pair of sides. If the di

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Question 906014: A gardener has 270 feet of fencing and wants to fence in a rectangular garden and then divide it into two plots with a piece of fencing parallel to one pair of sides.
If the dividing fence is x feet long, and y is the length of the side perpendicular to the dividing fence, write an equation for the total amount of fencing used in terms of x and y.
Fencing =
Write the area A of the garden as a function of x.
A(x) =
What are the dimensions of the largest garden (in area) that the gardener can enclose?
Width =
Length =
Please provide inches or feet
Thank you

Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
The gardener has then 3 lengths of x and 2 lengths of y. The fence material is distributed as 3x%2B2y=270.

A(x)? The area.
A=xy.
Use the fence length account equation to eliminate y.
2y=270-3x

y=%28270-3x%29%2F2
-
A%28x%29=x%28270-3x%29%2F2

A%28x%29=%28270x-3x%5E2%29%2F2

highlight%28A%28x%29=135x-%283%2F2%29x%5E2%29.

You can find the maximum area if you want; set A%28x%29=0 and solve for x.