I googled it, if you are curious they don't actually line up in the rectangle because the slopes of the hypotenuses are different. This leaves a long, thin parallelogram in the middle with an area of 1 square unit, the difference between the two.
The squares are not equal among themselves after cutting and connection in other order. And multiplication is fair only for equal objects. Use your brains!
See here for a really good explanation as well as a more accurate ending picture (the 5x13 one) that really shows the trick.
mathematicscentre.com/taskcentre/155_6465.htm
Angles are not same. First cut is 3 squares by 8 squares. Second cut is 2 squares by 5 squares. Arctan 3/8 does not equal arctan 2/5. Slight difference.
Just look between green and blue, red and green, red and orange. The squares aren't perfect. It's just like the "infinite chocolate", it's an illusion.
When it gets to 65, you take one away and the put the remaining boxes back into a 64 cube and start again and keep collecting and saving the extra ones until you have enough to build a house with which you will have done for free!
mathematicscentre.com/taskcentre/155_6465.htm