Let's begin by identifying key information given to us:
[tex]\begin{gathered} PQ\mleft\Vert \mright?BC \\ AP=9 \\ PB=18 \\ AQ=x \\ QC=10 \end{gathered}[/tex]
Since PQ & BC are similar, we will use the proportion to solve for x
[tex]\begin{gathered} \frac{PB}{AP}=\frac{QC}{AQ}\Rightarrow\frac{PB}{AP}=\frac{QC}{x} \\ \frac{PB}{AP}=\frac{QC}{x} \\ \Rightarrow\frac{18}{9}=\frac{10}{x} \\ \text{Cross multiply, we have:} \\ 18\cdot x=10\cdot9 \\ 18x=90 \\ x=\frac{90}{18}=5 \\ x=5 \end{gathered}[/tex]
Hence, B is the correct answer
