"The length is 6 meters longer than the width" means l = 6 + w.
Using the perimeter formula, we have
[tex]\begin{gathered} P=2(w+l) \\ 114=2(w+6+w) \\ \frac{114}{2}=2w+6 \\ 57-6=2w \\ w=\frac{51}{2} \\ w=25.5 \end{gathered}[/tex]Then,
[tex]l=6+25.5=31.5[/tex]