Ratio of triangles areas

A Heronian triangle ABC has the following dimensions :
- BC = a = 203
- CA = b = 265
- AB = c = 372

We choose 3 points:
- point X on BC at a distance p of B
- point Y on AC at a distance q of A
- point Z on AB at a distance r of C
(p,q,r are integers)


For how many triples (p,q,r) the ratio Area(ABC)/Area(PQR) is an integer?

Answer format: Count/p,q,r // For the smallest ratio

You are given: 6/2,3,2 for the triangle (3,4,5)
[My timing: 10 sec]