2019 AIME II Problem 7

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.