|A right triangle where the sides are in the ratio of integers. (Integers are whole numbers like 3, 12 etc)|
If you multiply each side by an integer, the result will be another triple, demonstrating that there is an infinite number of them. Remember: it is the ratio of the lengths of the sides that counts, not the actual length. The units of measurement are thus irrelevant.
The smallest and perhaps best known triple, the 3:4:5 is explored in greater depth 3-4-5 Triangles.