  By employing a framework for the quasi-two-body decays in the perturbative
QCD (PQCD) factorization approach, we calculate the branching ratios of the
decays $B_{(s)} \to D (\rho(1450),\rho(1700))\to D \pi \pi$ with $D=(D_{(s)},
\bar{D}_{(s)})$. The pion vector form factor $F_\pi$, acquired from a {\it
BABAR} Collaboration analysis of $e^+ e^- \to \pi^+ \pi^-(\gamma)$ data, is
involved in the two-pion distribution amplitudes $\Phi^{I=1}_{\pi\pi}$. The
PQCD predictions for the branching ratios of the considered quasi-two-body
decays are in the range of $10^{-10} \sim 10^{-4}$. The PQCD predictions for
${\cal B}(B^0\to \bar{D}^0 (\rho^0(1450),\rho^0(1700)) \to \bar{D}^0
\pi^+\pi^-)$ agree well with the measured values as reported by LHCb if one
takes still large theoretical errors into account. Unlike the traditional way
of the PQCD approach, one can extract the decay rates for the two-body decays
$B_{(s)} \to D (\rho(1450),\rho(1700))$ from the results of the corresponding
quasi-two-body decays. The PQCD predictions for ${\cal B}(B_{(s)} \to D
\rho(1450))$ and ${\cal B}(B_{(s)} \to D \rho(770))$ are similar in magnitude:
an interesting relation to be tested by future experimental measurements.
