A Triangle from Three Parallels

Triangle $ABC$ has side lengths $AB=120$, $BC=220$, $AC=180$. Lines $\ell_A$, $\ell_B$, $\ell_C$ are parallel to $BC$, $AC$, $AB$ respectively, and the segments cut by $\triangle ABC$ on these lines have lengths $55$, $45$, $15$ respectively. Find the perimeter of the triangle bounded by $\ell_A$, $\ell_B$, $\ell_C$.