Let the length be represented by l and the width, w.
The question says that the length is 3 feet longer than the width. This means that
[tex]l=w+3[/tex]The perimeter of a rectangle is given as
[tex]2(w+l)=P[/tex]The perimeter of the sandbox is given as 22 feet.
Substituting the values for the perimeter and the length (w + 3) into the perimeter formula, we have
[tex]2(w+w+3)=22[/tex]Solving, we have
[tex]\begin{gathered} 2(2w+3)=22 \\ 2w+3=\frac{22}{2} \\ 2w=11-3 \\ 2w=8 \\ w=\frac{8}{2} \\ w=4 \end{gathered}[/tex]Now that we have the value for the width, we can calculate the length as
[tex]\begin{gathered} l=w+3 \\ l=4+3 \\ l=7 \end{gathered}[/tex]The length is 7 feet and the width is 4 feet.
