3 Rectangles + 1 Triangle = ?Geometry Level 5
Triangle \(ABC\) has integer side lengths. Rectangles \(BCDE, ACFG, ABHJ\) are constructed so that \(CD = AC + AB\), \(CF = AB + BC\), and \(BH = (AC + BC)^2\). If \([ABHJ] = [BCDE] + [ACFG]\), how many different values can \([ABC]\) have?
Details and assumptions
\([PQRS]\) refers to the area of figure \(PQRS\).