geometry - 20 right isosceles triangles into a square

Similar: Unlucky tiling: Arrange thirteen right isosceles triangles into a square

Five graded difficulty isosceles right triangle into square tilings

Two difficult "Seventeen right isosceles triangles into a square" tilings

The challenge is to fit the smallest $20$ integer-sided scaled right isosceles triangles into a square with diagonal $46$

For convenience, I list the areas of the triangles:

$1, 2, 4, 8, 9, 16, 18, 25, 32, 36, 49, 50, 64, 72, 81, 98, 100, 121, 128, 144$

There are four ways of doing it (not two as originally posted). A brave person it would be who tackled this by hand.

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:

Answer

Here are at least two solutions (up to reflection and rotation)

The trapezoid outlined in red can be flipped.

This is presumably the other "substantially different" solution (not counting the above trapezoid flip as different).