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.

All we really need to take away from the two lines is the angle between them, which is approximately 18.4349488229 degrees. Call this a.

Construct a circle with radius 30. The diameter is AB; C is on the circumference. Construct triangle ABC. D is the midpoint of AC and E is the midpoint of BC. When the angle between AE and BD is a, ABC is compliant with the description in the problem.

When that happens, the area of ABC is exactly 400.

Edited on December 8, 2014, 11:05 pm

Posted by broll on 2014-12-08 22:38:53