Step 1. Define the length
We will call the length of the rectangle x:
[tex]\text{LENGTH}=x[/tex]Step 2. Define the width
Since the width is 11 less than twice the length:
[tex]\text{WIDTH}=2x-11[/tex]Step 3. Use the formula for the perimeter of a rectangle:
[tex]\text{PERIMETER}=2(WIDTH)+2(LENGTH)[/tex]Substituting the value of the perimeter: 52.4, the width and length:
[tex]52.4=2(2x-11)+2(x)[/tex]Using distributive property on the right side:
[tex]52.4=4x-22+2x[/tex]And combining like terms in the right:
[tex]52.4=6x-22[/tex]Adding 22 to both sides:
[tex]\begin{gathered} 52.4+22=6x-22+22 \\ 74.4=6x \end{gathered}[/tex]Dividing both sides by 6:
[tex]\begin{gathered} \frac{74.4}{6}=\frac{6x}{6} \\ 12.4=x \end{gathered}[/tex]Thus, the width and length are:
[tex]\begin{gathered} \text{LENGTH}=x=12.4ft \\ \text{WIDTH}=2x-11=2(12.4)-11=24.8-11=13.8ft \end{gathered}[/tex]