Question

LM=7a MN=12aLM=56IF M is between L and N; find the value of the variable first then find LN

Answer 1

Sketch the line LN with point M between L and N.

Determine the value of by using segment LM.

`\begin{gathered} LM=7a \\ 56=7a \\ a=(56)/(7) \\ =8 \end{gathered}`

Determine the length of line LN by addition segment postulates.

`\begin{gathered} LN=LM+MN \\ =7a+12a \\ =19a \end{gathered}`

Substitute 8 for a in the equation to obtain the length LN.

`\begin{gathered} LN=19\cdot8 \\ =152 \end{gathered}`

Thus, value of variable a is 8 and LN = 152. Option B is correct.