# 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.

• What do you mean by "the median at point A"? Could you please clarify?

• I guess it means the line segment through A to the midpoint of BC. Right?

• Bounty is too low!

• This is a challenging question and one needs probably about 30 minutes to write a good solution. I also think the bounty is too low!