With the exception of mathematical equations, I don't see what the big deal with this puzzle is. The height of the green triangle is smaller than that of the red one, so when you switch the two, you have to readjust the orange and green shapes in the corner to match the height of the green triangle and the width of the red one.
Kent Frost is pretty much right here. But it's not just the height of the two triangles that's different, it's the ratio of the height to the base. Here's another link that explains the trick: http://www.grand-illusions.com/triangle1.htm