Link to next puzzle in this series:Five graded difficulty isosceles right triangle into square tilings
This problem has only one solution, and will be challenging by hand, but probably more satisfying. Computers allowed, probably challenging too. Not for the computer, but for the programmer.
The challenge is to arrange thirteen right isosceles triangles of the following areas into a $36\times 36$ square with no gaps or overlaps.
$2, 4, 8, 18, 32, 64, 72, 98, 128, 144, 196, 242, 288$
By way of illustration/clarification, here are the right isosceles triangles of area
$1, 2, 4, 9, 16, 18, 50$
arranged into a $10\times 10$ square:
If you can solve this with scalene right triangles of the correct area... I'll accept that too.