  We present a modified version of the definition of property RD for discrete
quantum groups given by Vergnioux in order to accommodate examples of
non-unimodular quantum groups. Moreover we extend the construction of spectral
triples associated to discrete groups with length functions, originally due to
Connes, to the setting of quantum groups. For quantum groups of rapid decay we
study the resulting spectral triples from the point of view of compact quantum
metric spaces in the sense of Rieffel.
