Triangle \(\triangle{ABC}\) has side lengths \(AB=120,BC=220\), and \(AC=180\). Lines \(\ell_A,\ell_B\), and \(\ell_C\) are drawn parallel to \(\overline{BC},\overline{AC}\), and \(\overline{AB}\), respectively, such that the intersections of \(\ell_A,\ell_B\), and \(\ell_C\) with the interior of \(\triangle ABC\) are segments of lengths \(55,45\), and \(15\), respectively. Find the perimeter of the triangle whose sides lie on lines \(\ell_A,\ell_B\), and \(\ell_C\).