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If OP = 14, SQ = 7, and QR = 24, find PR. 

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

Sagot :

Given that

[tex]\begin{gathered} OP=14 \\ SQ=7 \\ QR=24 \\ PR=\text{?} \end{gathered}[/tex]

Using the method of the ratio of similar figures,

Which says

[tex]\frac{OP}{SQ}=\frac{PR}{QR}[/tex]

Therefore,

[tex]\frac{14}{7}=\frac{PR}{24}[/tex]

Solving for PR

First of all, we will cross-multiply

[tex]\begin{gathered} 7\times PR=14\times24 \\ 7PR=14\times24 \end{gathered}[/tex]

Then, we will divide both sides by 7

[tex]\begin{gathered} \frac{7PR}{7}=\frac{14\times24}{7} \\ PR=2\times24=48 \\ \therefore PR=48 \end{gathered}[/tex]

Hence,

[tex]PR=48\text{units}[/tex]

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