Finding the area of a right angle triangle given the equations of median lines and the length of the hypotenuse
There is a right triangle ABC in the plane, of which angle C is a right angle. If the the line segment through A to the midpoint of BC is on the straight line x+y=0, the line segment through B to the midpoint of AC is on x+2y=0, and the length of AB is 36, find the area of the triangle ABC.
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