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

If OP 14 SQ 7 And QR 24 Find PQ class=

Sagot :

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]

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