  In this work, we prove that any triangle whose three sidelengths are
integers, cannot have all of its three medians also having integral
lengths.This is done in Proposition 2.In Section 5, we give
precise(i.e.necessary and sufficient)conditions for a nonisosceles,
integer-sided triangle to have two integral medians.In Section 3, we offer
parametric descriptions of three special families of integer-sided
triangles.The first family consists of all Pythagorean triangles whose medians
to their hypotenuses is integral. The other two medians (to the two legs)of any
Pythagorean triangle are irrational, a proof of this fact can be found in
reference 4 of this paper.The second family consists of all integer-sided
isosceles triangles, whose only integral median is the one contained between
the two sides of equal length. Finally, the third family consists of all
isosceles integer-sided triangles with the two medians of equal length;having
integer length.
