Notice that triangles QRS and YRZ are similar, therefore:
[tex]\frac{YZ}{QS}=\frac{YR}{QR}=\frac{1}{2}\text{.}[/tex]
Substituting YZ=x+2, QS=3x-8, and solving for x we get:
[tex]\begin{gathered} \frac{x+2}{3x-8}=\frac{1}{2}, \\ 2(x+2)=3x-8, \\ 2x+4=3x-8, \\ x=12. \end{gathered}[/tex]
Answer: Option C).
