Since the triangles are similar that means that:
[tex]9=6x[/tex]
where x is the factor that tajes triangle GHK to triangle JMP. Solving for x we have:
[tex]\begin{gathered} 9=6x \\ x=\frac{9}{6} \\ x=\frac{3}{2} \end{gathered}[/tex]
Now, we know that a similarity transformation takes the perimter to the original tirangle to the new one like:
[tex]P^{\prime}=xP[/tex]
where P' is the perimeter of triangle JMP and P the perimeter of triangle GHK. Then:
[tex]P^{\prime}=\frac{3}{2}\cdot39=58.5[/tex]
Therefore the perimter of triangle JMP is 58.5 inches.
