Let (Formula presented.) be positive integers such that (Formula presented.) and (Formula presented.) be a tripartite graph with parts (Formula presented.) such that (Formula presented.). Denote the edge densities of (Formula presented.) and (Formula presented.) by (Formula presented.) and (Formula presented.), respectively. In this paper, we study edge density conditions for the existence of (Formula presented.) vertex-disjoint triangles in a tripartite graph. For (Formula presented.) we give an optimal condition in terms of densities (Formula presented.) for the existence of (Formula presented.) vertex-disjoint triangles in (Formula presented.). We also give an optimal condition in terms of densities (Formula presented.) for the existence of a triangle-factor in (Formula presented.).