Let triangle $ABC$ be a right triangle in the $xy$-plane with a right angle at $C_{}$. Given that the length of the hypotenuse $AB$ is $60$, and that the medians through $A$ and $B$ lie along the lines $y=x+3$ and $y=2x+4$ respectively, find the area of triangle $ABC$.
== See also ==
* [[American Invitational Mathematics Examination]]
* [[AIME Problems and Solutions]]
* [[Mathematics competition resources]]