Strange Squares

The mysterious extra square sneaks into the picture by hiding in a very clever place: in the thickness of the lines used to draw out the shapes. If the lines were drawn very thin, like they are in the image below, you can see that the shapes don't line up perfectly.

Note the slope of the line dividing the rectangle in two. It's 5/13, or .3486. Now measure the slope of the hypotenuse of triangle 3, it's 3/8 or .375 exactly. Since they don't match, the upper portion of the rectangle must not be lining up perfectly with the lower portion. You can see this more clearly below: