Let the length of the wall be l.
The width is 4ft less than its length.
Therefore, the width is l - 4.
The wall is rectangular, therefore
[tex]\text{ area of wall = length}\times\text{ width}[/tex]Hence,
[tex]\begin{gathered} l(l-4)=140 \\ l^2-4l=140 \\ \Rightarrow l^2-4l-140=0 \\ l^2+10l-14l-140=0 \\ \Rightarrow l(l+10)-14(l+10)=0 \\ \Rightarrow(l-14)(l+10)=0 \\ \Rightarrow l-14=0,l+10=0 \\ \Rightarrow l=14,l=-10 \\ \text{ Since l cannot be negative, then the only possibility is} \\ l=14\text{ ft} \\ \end{gathered}[/tex]Hence, the length of the wall is 14 feet
