Question

If P is between L and A, PL = 6x + 24, PA = 12x - 6 and LA = 30x - 18, then x = ______ and LA = ___&&

Answer 1

To solve this problem, we have to use the definition of segment addition.

$LA=PL+PA$

Then, we replace the given expressions

$30x-18=6x+24+12x-6$

Now, we solve for x.

$\begin{gathered} 30x-6x-12x=24-6+18 \\ 12x=36 \\ x=\frac{36}{12} \\ x=3 \end{gathered}$

Hence, x = 3.

Let's find LA:

$30x-18=30\cdot3-18=90-18=72$

Hence, LA measures 72 units.