$a\+b \= c \+ 2 \sqrt{\frac{\left(c-a\right)\left(c-b\right)}{2}}$.

$\frac{\left(c-a\right)\left(c-b\right)}{2}$ is always a perfect square.

At most one of $a$, $b$, $c$ is a square.

Exactly one of $a$, $b$ is odd; $c$ is odd.

Exactly one of $a$, $b$ is divisible by 3.

Exactly one of $a$, $b$ is divisible by 4.

Exactly one of $a$, $b$, $c$ is divisible by 5.

The area  $A \= \frac{\mathrm{ab}}{2}$ is an even number.

By definition, $A$ is also congruent, that is, a positive integer which is the area of a right angled triangle with rational numbered side lengths.