posted by anonymous .
ABC is a triangle with AC=139 and BC=178. Points D and E are the midpoints of BC and AC respectively. Given that AD and BE are perpendicular to each other, what is the length of AB?
Since D, E bisect BC and AC respectively, we have
Let medians AD and BE meet at K.
Let KD=x, DE=y
since medians intersect each other at third points.
Consider right triangle AKE right angled at K:
Consider right triangle BKD,
4(1)-(2) to eliminate y:
Substitute x² in (2):
Finally, consider right triangle AKB: