We have the following:
A square has equal sides, therefore we make the following equality
[tex]\begin{gathered} x+7=3x+1 \\ 3x-x=7-1 \\ 2x=6 \\ x=3 \end{gathered}[/tex]
now, replacing:
[tex]\begin{gathered} LM=3+7=10 \\ MN=3\cdot3+1=9+1=10 \end{gathered}[/tex]
Therefore, the answer is option b
