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Answer :

we can establish a ratio since triangle MNQ is equals to triangle MLP.

[tex]\begin{gathered} \frac{NQ}{LP}=\frac{MQ}{PM} \\ \frac{6}{LP}=\frac{8}{12} \\ LP=\frac{72}{8} \\ LP=9\text{ inches} \end{gathered}[/tex]

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