Find area of triangle in a rectangle, its sides; given

In rectangle ABCD, points E and F are on sides AD and DC such that A-E-D and D-F-C. Areas of triangles are as follows: Tri. ABE = 180 sq. cm. ; Tri. BCF = 384 sq. cm. ; Tri. DEF = 60 sq. cm.; AB, BC, AE, FC, ED, DF are all positive integers. AB > BC Find: 1) Area of [] rectangle ABCD 2) Area of Tri. BEF. 3) side AB given AB - BC = 16 cm 4) side BC 5) Also find sides of the triangle BEF 6) You may verify area of the tri. obtained in 2) by Heron's formula. Do you find the lengths of segments (dimensions of triangles and reectangle) wonderful? It is the grace of Saint Saibaba, Shirdi, Maharashtra, India and Goddess Mahalaksmi that inspired me this sum.