Why don't these two identical math equations equal the same thing? (See picture.)

Once the gif started cutting the boxes into pieces, it’s all optical illusion. they changed the number of boxes in the rectangle with that little geometric magic.

Identical math equations do equal each other. The fallacy in this diagram is that there is an “apparency” of an added square. It’s not, really, but it does look that way.

Because they’re not the same.

There is a misleading slope to the diagonal. It is an optical illusion.
Solution

Gaps. If you look closely, you see that the second figure is not completely closed. This gap is the size of one square.

This is an old classic called Curry’s paradox, re-introduced by Martin Gardner in Scientific American in1956. The fallacy, of course, is that the big triangles are actually quadrilaterals, bent slightly convex or concave in either of two configurations to account for the ‘missing square’. Actually the slopes of component triangles are in a 24:25 ratio—close but not equal.