(C need not be the hypotenuse.)
To side C attach another right triangle with integer sides C, D & E.
On this new triangle attach another right triangle to either side D or E. Continue the process of attaching a new right triangle to the previous; creating a chain of right triangles.
Three further rules:
1. No side length may be repeated.
2. No triangles may overlap.
3. No side may have length over 10000.
How many triangles can you make in this chain?