The perimeter of a rectangle of width W and length L is given by:
[tex]P=2(W+L)[/tex]We have the expressions:
[tex]\begin{gathered} P=6x^2+6x+12 \\ W=2x^2+1 \end{gathered}[/tex]Then:
[tex]\begin{gathered} \frac{P}{2}=W+L \\ \\ L=\frac{P}{2}-W \end{gathered}[/tex]Using the expressions for P and W:
[tex]\begin{gathered} L=\frac{6x^2+6x+12}{2}-2x^2-1=3x^2+3x+6-2x^2-1 \\ \\ \therefore L=x^2+3x+5 \end{gathered}[/tex]