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)→ D (ρ(1450),ρ(1700))→ D ππ with D=(D_(s), D̅_(s)). The pion vector form factor F_π, acquired from a BABAR Collaboration analysis of e^+ e^- →π^+ π^-(γ) data, is involved in the two-pion distribution amplitudes Φ^I=1_ππ. The PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the range of 10^-10∼

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... ^-4. The PQCD predictions for B(B^0→D̅^0 (ρ^0(1450),ρ^0(1700)) →D̅^0 π^+π^-) 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)→ D (ρ(1450),ρ(1700)) from the results of the corresponding quasi-two-body decays. The PQCD predictions for B(B_(s)→ D ρ(1450)) and B(B_(s)→ D ρ(770)) are similar in magnitude: an interesting relation to be tested by future experimental measurements.