Can anyone explain to me how this conundrum works?
It’s not actually a triangle. In the first picture, the hypotenuse is caved in a little bit into the triangle. In the second picture, the hypotenuse is bulging outward. (Check the respective slopes of the hypotenuses of the two smaller rectangles). The difference between the caving in/bulging out makes up for the difference of the “missing square”.
Of course, the above parenthetical comment should be referring to triangles, not rectangles. Don’t know where that one came from.
Here’s a nice site with the explanation.
You may enjoy some of the other puzzles, etc there as well. 
I puzzled it out like this:- the top triangle is 2 by 5. For the bottom triangle to have the same angle of the hypotenuse it should be 3 by 7.5 Which, of course, it ain’t. Check out Ferris’ site. I like the one about the bomber.