Parallelepipedic Box

The parallelepipedic box of dimensions $2\times 3\times 6$ has a diagonal of 7.

A parallelepipedic box with integer sides has a diagonal of 100000.

Let x,y,z its dimensions with $x\le y\le z$.

Find all the possible triples x,y,z

Answer format: $count,\sum z$

[My timing: 10 sec]