I might have gone around the world to get this answer but here goes
I let
AP=AS=QC=CR=t
and
PB=BQ=RD=DS=g
I then used algebra to get an expression for the area of the triangles and put it equal to 200
from this I could get t in terms of g
Then you can use pythagoras to find QR squared and QP squared in terms of g
Then you can use pythagoras again to find PR.