A right rectangular prism P (i.e., a rectangular parallelpiped) has sides of integral length a,b,c, with a≤b≤c. A plane parallel to one of the faces of P cuts P into two prisms, one of which is similar to P, and both of which have nonzero volume. Given that b=1995, for how many ordered triples (a,b,c) does such a plane exist? geometry3D geometryprismcalculusintegrationratiorectangle