We present the first determination of the intrinsic triaxial shapes and three-dimensional physical parameters of both dark matter (DM) and the intracluster medium for the galaxy cluster A1689. We exploit the novel method we recently introduced in order to infer the three-dimensional physical properties in triaxial galaxy clusters by combining jointly X-ray and strong lensing data. We find that A1689 can be modeled as a triaxial galaxy cluster with DM halo axial ratios 1.24 +/- 0.13 and 2.37 +/- 0.11 on the plane of the sky and along the line of sight, respectively. We show that accounting for the three-dimensional geometry allows us to solve the discrepancy between the mass determined from X-ray and strong gravitational lensing observations. We also determined the inner slope of the DM density profile alpha; we measure alpha = 0.90 +/- 0.05 by explicitly accounting for the three-dimensional structure for this cluster, a value which is close to the cold dark matter (CDM) predictions, while the standard spherical modeling leads to the biased value alpha = 1.16 +/- 0.04. Our findings dispel the potential inconsistencies that arise in the literature between the predictions of the CDM scenario and the observations, providing further evidences that support the CDM scenario.