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 \(PQRS\).

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