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Thank you.

Well, all sides can be different, it is just that they have to they must have an integer value and they must be multiple numbers. (For example like 6 is integer number and is also a multiple number.)

Yes, I want to prove if sides a, b, c are integers and heigths k, i, j are also integers, then theese integers are all multiples. I believe I have to use triangle area formula and Pythagorean theorem, then compare the sides and heights of the triangle. I would start by selecting one side and...

Thank you for correcting me.

Like so.

I'm trying to prove that if the lengths of the sides of a triangle and the heights drawn to all sides are integers, then these integers are all multiples.

Yes. If the triangle has integer sides and integer heights (the heights also must multiples not primes), then I believe the area should also be integer, if I'm not wrong.

I tried to figure it out by proof by contradiction. I assumed wlog that one side is a prime number, which gave a contradiction, and I also found that such a triangle should be isosceles. Then I assumed wlog that one of the heights is a prime number and I also got a contradiction. Therefore, all...