Explanation
We are given the following information from the figure:
[tex]\begin{gathered} |QP|=x \\ |RQ|=12 \\ |RS|=18 \\ |ST|=16 \end{gathered}[/tex]
We are to determine the value of x. This can be achieved by using the formula below:
[tex]\begin{gathered} |RQ|\cdot|RP|=|RS|\cdot|RT| \\ where \\ |RP|=|RQ|+|QP| \\ |RT|=|RS|+|ST| \end{gathered}[/tex]
Using the formula above and substituting their corresponding values, we have:
[tex]\begin{gathered} 12(12+x)=18(18+16) \\ 12(12+x)=18(34) \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }12 \\ \frac{12(12+x)}{12}=\frac{18(34)}{12} \\ 12+x=51 \\ x=51-12 \\ x=39 \end{gathered}[/tex]
Hence, the value of |PQ| is 39.
