A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. You are given a triangle with side lengths of 11 cm, 13 cm, and 16 cm. Determine the length of the median that joins the side of length 16 cm and the opposite vertex.
Source: mathcontest.olemiss.edu 11/2/2009
Let . Let be the median joining vertex to the midpoint . From vertex draw altitude to side .
In right triangle , by the Pythagorean theorem we have