This should be a little trickier.
Using $20$ rectangles of aspect ratio $1:2$, make two squares.
2,3,7,12,16 in both squares.
And split this list among the two squares:
In other words, the first square uses all five from the first list and five from the second. The second square uses the first list plus the other five from the second list. Sizes
2,3,7 means $2\times4$, $3\times6$, $7\times14$ etc
As usual, no gaps or overlaps.
A computer would spoil it. But it's probably fairly tough by hand.