If the sides of a triangle are 6,8 and 10, and if we know that the shorter side of a similar triangle is 15 the we know that the this relation has to be true so:
[tex]\frac{15}{6}=\frac{x}{8}=\frac{y}{10}[/tex]So we can find x and y that are the missing sides of the similar triangle so:
[tex]\begin{gathered} \frac{x}{8}=\frac{15}{6} \\ x=\frac{15\cdot8}{6} \\ x=20 \end{gathered}[/tex]and for y:
[tex]\begin{gathered} \frac{y}{10}=\frac{15}{6} \\ y=\frac{15\cdot10}{6} \\ y=25 \end{gathered}[/tex]So the perimeter (P) will be:
[tex]\begin{gathered} P=15+20+25 \\ P=60 \end{gathered}[/tex]