Sketch the line LN with point M between L and N.
Determine the value of by using segment LM.
[tex]\begin{gathered} LM=7a \\ 56=7a \\ a=\frac{56}{7} \\ =8 \end{gathered}[/tex]
Determine the length of line LN by addition segment postulates.
[tex]\begin{gathered} LN=LM+MN \\ =7a+12a \\ =19a \end{gathered}[/tex]
Substitute 8 for a in the equation to obtain the length LN.
[tex]\begin{gathered} LN=19\cdot8 \\ =152 \end{gathered}[/tex]
Thus, value of variable a is 8 and LN = 152. Option B is correct.
