imc

Let $x$ be the length of the first side. The lengths of the sides are: $x$, $3x$, and $15$. By the Triangle Inequality, $3x<x+15$ $2x<15$ $x<\frac{15}{2}$ The greatest integer satisfying this inequality is $7$. So the greatest possible perimeter is $7+3\cdot 7+15=\boxed{43}$