Consider a right angled triangle ABC situated in the XY plane, where AB is the hypotenuse.

Given that:

(i) AB = 60, and:
(ii) The medians through A and B lie along the lines y=x+3 and y=2x+4 respectively.

Determine the area of triangle ABC.

I'm pretty sure this is the only solution. 

Area of triangle ≈9.40445

A=(-16.20718,-13.20718)
B=(16.35558,37.07117)
C=(-3.32841,-17.86339)

Trying to solve analytically eventually led to a quartic polynomial with terms in the millions.  One of them did turn out to be correct, I think.

Edit:  The area above does not take my scale into account.
A distance on 1 on my graph was only .15333 cm.
9.40445/1.5333² = 400.018

Edited on December 10, 2014, 10:48 am

Posted by Jer on 2014-12-08 06:51:09