3 Rectangles + 1 Triangle = ?

Geometry Level 5

Triangle ABCABC has integer side lengths. Rectangles BCDE,ACFG,ABHJBCDE, ACFG, ABHJ are constructed so that CD=AC+ABCD = AC + AB, CF=AB+BCCF = AB + BC, and BH=(AC+BC)2BH = (AC + BC)^2. If [ABHJ]=[BCDE]+[ACFG][ABHJ] = [BCDE] + [ACFG], how many different values can [ABC][ABC] have?

Details and assumptions

[PQRS][PQRS] refers to the area of figure PQRSPQRS.

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