Answer
The answer is: 105 ft in length and 120 ft in width.
Work Step by Step
We assign the variables:
$l=$ length of the yard
$w=$ width of the yard
Step 1:
Find the equations that represent the problem.
The formula for the perimeter of a rectangle (not including the side of the house that is not fenced) is
$P=l+2w$ -> Eq. 1
We can get the second equation from the wording in the problem.
From " The length of fence opposite the house is 15 ft less than either of the other two sides", we get:
$l=w-15$ -> Eq. 2
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute Eq. 2 into Eq, 1
$w-15+2w=345$
$3w=345+15$
$3w=360$
$w=\frac{360}{3}$
$w=120$ ft
-> Substitute the value for w into Eq. 2
$l=120-15$
$l=105$ ft
Step 3:
The answer is: 105 ft in length and 120 ft in width.
