Question

module 1 application problem #2
for this problem you will determine the cost to put a
fence around the perimeter of the backyard you worked
on in problem #1. to do this, you need to find the
perimeter of the part of the yard that will be fenced. the
city you live in requires that your fence be 2 feet away
from your property line on all sides.
step 1:
write an equation for the width of the fenced
sides using the variable w from problem 1.
if the width of the yard is w, what is the
width of the fenced area?
width of fenced area = w -
step 2:
assume there is a house that will take the place
of one width of the fenced area as shown in the
picture to the right. how can you describe the
length of the fenced area in terms of w using
the same l from problem 1?
if the length of
the entire yard is = w +
then the length of
the fenced yard is = w + -
step 3:
find the expression for the total length of fencing
you will need by adding up the fenced sides.
step 4:
if the fencing you plan to use is
$6 per linear foot, write an
expression for how much the
fencing will cost.
step 5:
what is the area of your backyard
that is fenced?

Explanation:

Step1: Width of the fenced area

Since the fence is 2 feet away from the property line on both sides for the width.
Width of Fenced Area \(=W - 2 - 2=W - 4\)

Step2: Length of the fenced yard

For the length, there is no house - related deduction (assuming the house is on the width side). If we assume the original length variable is related to the entire yard. If we consider the addition due to the 2 - foot fence on one side (assuming the other side is adjacent to the house for the length in the problem's context).
If the Length of the entire yard is \(L\) (but since we are to use the same \(L\) concept as in problem 1, and considering the 2 - foot fence on one non - house side).
Then the Length of the FENCED yard is \(L+2\) (assuming the house takes up one side of the length in the original problem 1 concept and we add 2 feet for the non - house side fence)

Step3: Total length of fencing

The fenced sides: two lengths and one width (because the house takes the place of one width).
Total length of fencing \(=2(L + 2)+(W - 4)=2L+4 + W-4=2L+W\)

Step4: Cost of fencing

If the cost is \(C\) and the cost per foot is \(\$6\), and the length of fencing is \(2L + W\)
\(C=6(2L + W)=12L+6W\)

Step5: Area of the fenced yard

Area \(A=(L + 2)(W - 4)=LW-4L + 2W-8\)

Answer:

• Step 1: \(4\)
• Step 2: \(2\), \(2\), \(0\) (assuming \(L\) is the original length variable from problem 1 and the second subtraction is \(0\) as there is no house - related length deduction in the fenced length calculation based on the problem's description)
• Step 3: \(2L + W\)
• Step 4: \(C = 12L+6W\)
• Step 5: \(A=LW-4L + 2W - 8\)