Suppose there's a right-angled triangle inside a rectangle in the following way:

![four right-angled triangles image](https://i.stack.imgur.com/sTdn0.png)

(just take any right-angled rectangle, "rotate" it and draw a rectangle around it)

There are four right-angled triangles in that image.

Does there exist a triangle and rectangle combo so that all the resulting triangles have [Pythagorean triples](http://en.wikipedia.org/wiki/Pythagorean_triple) as their sides?