Packing Pythagorean L's

Every square of integer length can be cut into a number of L's: .

For a pythagorean triple a2 + b2 = c2, can the L's from an a x a square and a b x b square can be packed into a c x c square? The following pictures show that this is sometimes possible. There are 3 infinite families of packings illustrated below.

32 + 42 = 52
52 + 122 = 132
72 + 242 = 252

42 + 32 = 52
82 + 152 = 172
122 + 352 = 372
122 + 52 = 132
282 + 452 = 532

There's some more info on Joe Fields' Puzzle Page.