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By employing a framework for the quasi-two-body decays in the perturbativeQCD (PQCD) factorization approach, we calculate the branching ratios of thedecays $B_{(s)} \to D (\rho(1450),\rho(1700))\to D \pi \pi$ with $D=(D_{(s)},\bar{D}_{(s)})$. The pion vector form factor $F_\pi$, acquired from a {\itBABAR} Collaboration analysis of $e^+ e^- \to \pi^+ \pi^-(\gamma)$ data, isinvolved in the two-pion distribution amplitudes $\Phi^{I=1}_{\pi\pi}$. ThePQCD predictions for the branching ratios of the considered quasi-two-bodydecays 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 onetakes still large theoretical errors into account. Unlike the traditional wayof 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 correspondingquasi-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.

Quasi-two-body decays $B_{(s)} \to D (\rho(1450),\rho(1700)) \to D \pi \pi$ in the perturbative QCD factorization approach