Question

What is the value of x, given that PO is congruent to BC

Answer 1

Let's begin by identifying key information given to us:

`\begin{gathered} PQ\mleft\Vert \mright?BC \\ AP=9 \\ PB=18 \\ AQ=x \\ QC=10 \end{gathered}`

Since PQ & BC are similar, we will use the proportion to solve for x

`\begin{gathered} (PB)/(AP)=(QC)/(AQ)\Rightarrow(PB)/(AP)=(QC)/(x) \\ (PB)/(AP)=(QC)/(x) \\ \Rightarrow(18)/(9)=(10)/(x) \\ \text{Cross multiply, we have:} \\ 18\cdot x=10\cdot9 \\ 18x=90 \\ x=(90)/(18)=5 \\ x=5 \end{gathered}`

Hence, B is the correct answer