Question

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

Answer 1

The value of PQ is;

`PQ=24`

Step-by-step 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;

`(OP)/(SQ)=(PR)/(QR)`

Substituting the given values;

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

Therefore, the value of PQ is;

`PQ=24`