The multihadron decays Lambda(0)(b) -> D(+)p pi(-)pi(-) and Lambda(0 )(b)-> D-*+p pi(-)pi(-) are observed in data corresponding to an integrated luminosity of 3fb(-1), collected in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV by the LHCb detector. Using the decay Lambda(0)(b) -> Lambda(+)(c)pi(+)pi(-)pi(-) as a normalisation channel, the ratio of branching fractions is measured to be

B(Lambda(0)(b) -> D(+)p pi(-)pi(-))/B(Lambda(0)(b) -> Lambda(+)(c)pi(+)pi(-)pi(-)) x B(D+ -> K-pi(+)pi(+))/B(Lambda(+)(c)-> pK(-)pi(+)) = (5.35 +/- 0.21 +/- 0.16) %,

where the first uncertainty is statistical and the second systematic. The ratio of branching fractions for the Lambda(0)(b)-> D-*+p pi(-)pi(-) and Lambda(0)(b) -> D(+)p pi(-)pi(-) decays is found to be

B(Lambda(0)(b)-> D-+p pi(-)pi(-))/B(Lambda(0)(b) -> D(+)p pi(-)pi(-)) x (B(D-+-> D+pi(0)) + B(D (*)+-> D- (+)gamma)) = (61.3 +/- 4.3 +/- 4.0) %.