If two shapes are similar, they are scaled by some factor. In other words, you have
[tex]AB = k\cdot ED,\quad AC = k\cdot DF,\quad BC = k\cdot EF[/tex]
In particular, we know that
[tex]BC = 15 = k\cdot 5 = EF[/tex]
And we deduce [tex]k=3[/tex]
So, the perimeter of ABC is
[tex]AB+BC+AC = 3ED+3EF+3DF = 3(ED+EF+DF)[/tex]
So, the perimeter of ABC is three times the perimeter of DEF, and thus it's
[tex]12\cdot 3 = 36[/tex] feets
