8
Explanation
here we have 2 congruent triangles
APQ and ABC
as the proportion is the same(red length over blue length)
[tex]\begin{gathered} \frac{x}{12}=\frac{(12+x)}{30} \\ \text{cross multiply} \\ 30\cdot x=(12+x)\cdot12 \\ 30x=144+12x \\ \text{subtract 12 x in both sides} \\ 30x-12x=144+12x-12x \\ 18x=144 \\ \text{divide both sides by 18} \\ \frac{18x}{18}=\frac{144}{18} \\ x=8 \end{gathered}[/tex]
I hope this helps you
