Since ΔPQR is similar to ΔXYZ:
[tex]k\cdot PQ=XY[/tex]Where:
k = Scale factor
so:
[tex]\begin{gathered} k\cdot5=30 \\ solve_{\text{ }}for_{\text{ }}k\colon \\ k=\frac{30}{5} \\ k=6 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} k\cdot PR=XZ \\ XZ=6\cdot6=36 \\ ------ \\ k\cdot QR=YZ \\ YZ=6\cdot10=60 \end{gathered}[/tex]Since the perimeter is the sum of the sides:
[tex]P=XY+XZ+YZ=60+36+30=126\operatorname{cm}[/tex]