We report measurements of the branching fractions of the decays Lambda(+)(c) -> Sigma(+)pi(-)pi(+), Lambda(+)(c) -> Sigma(0)pi(+)pi(0) and Lambda(+)(c) -> Sigma(+)pi(0)pi(0) relative to the reference channel Lambda(+)(c) -> pK(-)p(+). The analysis is based on the full data sample collected at and near the gamma(4S) resonance by the Belle detector at the KEKB asymmetric-energy ethorne-collider, corresponding to an integrated luminosity of 711 fb(-1). We measure B(Lambda(+)(c) -> Sigma(+)pi(-)pi(+))/B(Lambda(+)(c) -> pK(-)pi(+)) = 0.719 +/- 0.003 +/- 0.024, B(Lambda(+)(c) -> Sigma(0) pi(+)pi(0))/B(Lambda(+)(c) -> pK(-)pi(+)) = 0.575 +/- 0.005 +/- 0.036 and B(Lambda(+)(c) -> Sigma(+)pi(0)pi(0))/B(Lambda(+)(c) -> pK(-)pi(+)) = 0.247 +/- 0.006 +/- 0.019. The listed uncertainties are statistical and systematic, respectively.