In rectangle ANHG, OP, PQ, and QR are mutually perpendicular and O is the midpoint of AN. If GH = 36 and GR =

Note that AN =  36

And since O  is the midpoint  of  AN, then  AO  = 18

And 

GR  = 2RH

So

GR + RH  =  36

2RH + RH  =  36

3RH   = 36 

RH  = 12 

So GR  =  24

So

GR  - AO  =  PQ

24  -  18   =  PQ  =  6