Why must one side of a right triangle be an even number?

Answer 1

Obviously you have something specific in mind, i.e. some other conditions.

For example a right triangle with legs of 1 and 3 has hypotenuse = sqrt(10)...no even number there.

However, maybe you are thinking about Pythagorean triples.

Set a = m² - n² and b = 2mn.

Then if c² = m² + n²

a,b and c are Pythagorean triples and every Pythagorean triple can be created in this way.

(BTW, I have never seen a proof of this statement, but I believe it is correct).

This answers your question!