Given that
[tex]\begin{gathered} OP=14 \\ SQ=7 \\ QR=24 \\ PR=\text{?} \end{gathered}[/tex]
Using the method of the ratio of similar figures,
Which says
[tex]\frac{OP}{SQ}=\frac{PR}{QR}[/tex]
Therefore,
[tex]\frac{14}{7}=\frac{PR}{24}[/tex]
Solving for PR
First of all, we will cross-multiply
[tex]\begin{gathered} 7\times PR=14\times24 \\ 7PR=14\times24 \end{gathered}[/tex]
Then, we will divide both sides by 7
[tex]\begin{gathered} \frac{7PR}{7}=\frac{14\times24}{7} \\ PR=2\times24=48 \\ \therefore PR=48 \end{gathered}[/tex]
Hence,
[tex]PR=48\text{units}[/tex]
