Fit the board into the hole

Question

How can you divide the board into exactly $2$ equally-shaped and sized pieces such that it fits the hole?

Bonus: Can you do the same problem in $3$ pieces, such that one of the pieces of the board has the sides of a square? If no, then what is the minimum number of pieces you have to make to do so?
Checkmark goes to the one who solves both parts :) .
Edit :- Forgot to mention that in the case of $3$ pieces, the square piece will be one of them, and the other two pieces will be equally-shaped and sized.

Bass · Accepted Answer

Assuming the picture is a bit off (seems like a safe assumption given that the areas don't quite match), I'm going to assume that the rectangles are scaled in

Some nice integer side lengths that achieve these proportions are

These particular shapes allow for this interesting dissection:

All the horizontal bits are supposed to be of the same length (5 units). For clarity I marked the lengths of the vertical sides (in units of one fifth of the height of the thinner rectangle) so it's easier to verify that the widths match in the rearranged shape too.

Pspl · Answer

Is the following the solution for the 2-piece problem?

Regarding the 3-piece puzzle, I'm not sure if the following solution will meet your criteria:

Fit the board into the hole

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