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Plug the side lengths into the Pythagorean theorem in place of a and b. If a2 + b2 = c2, it's a right triangle. C needs to be an integer, so c2 will be a perfect square.
Those ones, there!
There cannot be an integral set of values. The lengths need to be in the ratio 1 : sqrt(3) : 2.
It is a trapezoid that has one set of opposite parallel lines of different lengths.