To solve this problem, we have to use the definition of segment addition.
[tex]LA=PL+PA[/tex]
Then, we replace the given expressions
[tex]30x-18=6x+24+12x-6[/tex]
Now, we solve for x.
[tex]\begin{gathered} 30x-6x-12x=24-6+18 \\ 12x=36 \\ x=\frac{36}{12} \\ x=3 \end{gathered}[/tex]
Hence, x = 3.
Let's find LA:
[tex]30x-18=30\cdot3-18=90-18=72[/tex]
Hence, LA measures 72 units.
