Extracted text: A(x)
(8,192)
House
Figure 1
Figure 2
Tessa has 48 ft of fencing available to...

Question

Extracted text: A(x)
(8,192)
House
Figure 1
Figure 2
Tessa has 48 ft of fencing available to construct a fence that will divide her garden into two rectangular sections. Her house forms one side of the garden and a represents the width, as shown in Figure 1.
(a) Express the total area of the two sections as a function of x.
A(z) =
(b) Find the domain of the function. Write your answer as a compound inequality involving x.
Domain of A(z):
(c) Using the graph of A(x) shown in Figure 2, determine the dimensions that yield the maximum area.
Width:
ft
Length:
ft

Ajay · Accepted Answer

Solutions 
(a) A(x) can be obtained by knowing the rectangle's perimeter.
As you can see here, the perimeter of the lawn is:
3x + y = 48
because there are 3 x's and 1 y's, while the total perimeter is 48 ft.
 
Now, to find A(x), we use the are the formula of a rectangle in which:
A(x) = L x W
We know that W = x
 
To get the Length, we can use the perimeter of the lawn:

A(x) (8,192) House Figure 1 Figure 2 Tessa has 48 ft of fencing available to construct a fence that will divide her garden into two rectangular sections. Her house forms one side of the garden and a...

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