306 The area of a triangle
Appendix: A famous unsolved problem
Find a Heron triangle whose medians have integer lengths. This is a
famous unsolved problem. See [Guy, Problem D21]. The triangle with
sides 136, 170, 174 have medians 158, 131, 127. But it is not a Heron
triangle. It has an area.
Buchholz and Rathbun have found an infinite set of Heron triangles
with two integer medians. Here is the first one.
Leta=52,b= 102, andc= 146.
Verify that this triangle is Heron and find the lengths of the medians.