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!

  • 7-10$ is fair bounty

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  • This took me over an hour to answer. I was hesitant to answer the question, but I thought this might be the first time you are asking a question here, so I decided to answer. Please offer higher bounties in the future; otherwise, your questions may not get answered.

The answer is accepted.