Question

If OP = 14, SQ = 7, and QR = 24, find PQ

Answer 1

Answer:

The value of PQ is;

$PQ=24$

Explanation:

Given the figure in the attached image;

$\begin{gathered} OP=14 \\ SQ=7 \\ QR=24 \end{gathered}$

We can see from the figure that the triangle RSQ is similar to the triangle ROP.

So their corresponding sides are proportional;

$\frac{OP}{SQ}=\frac{PR}{QR}$

Substituting the given values;

$\begin{gathered} \frac{OP}{SQ}=\frac{PR}{QR} \\ \frac{14}{7}=\frac{PQ+24}{24} \\ 2(24)=PQ+24 \\ PQ=48-24 \\ PQ=24 \end{gathered}$

Therefore, the value of PQ is;

$PQ=24$