A scalene trapezoid with integer side-lengths has perimeter 10; find its height

I have a problem that I encountered on a math competition, but I don't know how to solve it. Can someone help me?
A scalene trapezoid ABCD with bases AB and CD has a perimeter of 10 centimeters. All the side lengths are integer numbers. Find the height of this trapezoid in simplest radical form.
No, I don't need the answer, just the solution.

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