Let's solve the problem step by step.
### Step 1: Understanding the Problem
Stanley is building a rectangular fence with a perimeter of 44 feet. The width is two less than half the length.
### Step 2: Formulating the Equations
The perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[ P = 2 \times ( \text{length} + \text{width} ) \][/tex]
Given that the width is two less than half the length, let:
[tex]\[ l = \text{length} \][/tex]
[tex]\[ w = \text{width} \][/tex]
From the problem, the width [tex]\( w \)[/tex] can be written as:
[tex]\[ w = \frac{l}{2} - 2 \][/tex]
### Step 3: Setting Up the Equation
The given perimeter equation can be written as:
[tex]\[ 2 \times (l + w) = 44 \][/tex]
Now, substitute the expression for the width [tex]\( w \)[/tex] into the perimeter equation:
[tex]\[ 2 \times \left( l + \left( \frac{l}{2} - 2 \right) \right) = 44 \][/tex]
### Step 4: Solve for Length ( [tex]\( l \)[/tex] )
Simplify the equation:
[tex]\[ 2 \times \left( l + \frac{l}{2} - 2 \right) = 44 \][/tex]
[tex]\[ 2 \times \left( \frac{2l + l - 4}{2} \right) = 44 \][/tex]
[tex]\[ 2 \times \left( \frac{3l - 4}{2} \right) = 44 \][/tex]
[tex]\[ 3l - 4 = 44 \][/tex]
[tex]\[ 3l = 48 \][/tex]
[tex]\[ l = 16 \][/tex]
Therefore, the length of the fence is [tex]\( l = 16 \)[/tex] feet.
### Step 5: Solve for Width ( [tex]\( w \)[/tex] )
Using the expression for width:
[tex]\[ w = \frac{l}{2} - 2 \][/tex]
[tex]\[ w = \frac{16}{2} - 2 \][/tex]
[tex]\[ w = 8 - 2 \][/tex]
[tex]\[ w = 6 \][/tex]
Therefore, the width of the fence is [tex]\( w = 6 \)[/tex] feet.
### Conclusion
The width of the fence is 6 feet.
