Answer:
The value of PQ is;
[tex]PQ=24[/tex]
Explanation:
Given the figure in the attached image;
[tex]\begin{gathered} OP=14 \\ SQ=7 \\ QR=24 \end{gathered}[/tex]
We can see from the figure that the triangle RSQ is similar to the triangle ROP.
So their corresponding sides are proportional;
[tex]\frac{OP}{SQ}=\frac{PR}{QR}[/tex]
Substituting the given values;
[tex]\begin{gathered} \frac{OP}{SQ}=\frac{PR}{QR} \\ \frac{14}{7}=\frac{PQ+24}{24} \\ 2(24)=PQ+24 \\ PQ=48-24 \\ PQ=24 \end{gathered}[/tex]
Therefore, the value of PQ is;
[tex]PQ=24[/tex]
