Pythagorean Tiles (num 139) for next week

Let $(a,b,c)$(A,B,C) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length $c$C.

For example, $(3,4,5)$(3,4,5) triangles can be placed together to form a 5$5$ by 5$5$ square with 1 a 1$1$ by $1$ hole in the middle and it can be seen that the 5$5$ by 5$5$ square can be tiled with twenty-five $1$1 by 1$1$ squares.

However, if $$(5,12,13)(5,12,13) triangles were used then the hole would measure $7$7 by 7$7$ and these could not be used to tile the 13$13$ by 13$13$ square.

Given that the perimeter of the right triangle is less than one-hundred million, how many Pythagorean triangles would allow such a tiling to take place?