Triangles have been studied for many years.

This statement was presumably true even when the above image was created circa 1800 B.C. on what is now known as the Rhind papyrus. Problem 51 above refers to a calculation of the area of a triangular plot of land.

Number theorists have long found triangles to provide a rich source of interesting problems. One can ask for triangles with rational sides and rational area. Alternately, one can ask for any of the altitudes to be rational. Or for that matter the medians, angle bisectors or whatever your favourite cevian happens to be.

Examples of such triangles can be found in On Triangles with rational altitudes, angle bisectors and medians.