SOLUTION: Tessa has 56 ft of fencing available to construct a fence that will divide her garden into three rectangular sections. Her house forms one side of the garden. Determine the largest

Question 1130353: Tessa has 56 ft of fencing available to construct a fence that will divide her garden into three rectangular sections. Her house forms one side of the garden. Determine the largest total area that can be enclosed.
Found 2 solutions by addingup, josgarithmetic:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
2L + 2W = 56
Since the house forms one side:
2L + W = 56 (you can take out one Length or one Width, it doesn't matter)
W = 56 - 2L We'll use this value for W below.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
L*W = Area (substitute for W):
L*(56-2L)= Area
56L - 2L^2 = Area
now let's call Area y and the length x and rewrite, so we have:
y = -2x^2 + 56x
x = -(b/2a) in this formula for the axis of symmetry, our a = -2 and our b = 56:
x = -56/(2(-2))
x = 14
F(14) = -2(14)^2+56(14)
F(14} = -392 + 784
F(14) = 392 this is the maximum area we can get
L = 56-2(14)
L = 56-28
L = 28
The largest total area that can be enclosed will be 14 feet wide and 28 feet long, giving a total area of 28*14 = 392 square feet

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
THREE RECTANGULAR SECTIONS.
Dimensions x and y for the entire garden

Let y be the length of the house to use for one whole side of the garden.
If the two divider fence parts are parallel to the x dimension, then:

Formula for garden area, A

You can use this formula to find the x for the maximum A, and use result to find y. (Maximum occurs in exact middle of the two zeros of A).
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