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

If OP = 14, SQ = 7, and QR = 24, find PQ-example-1

1 Answer

3 votes

Answer:

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

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