A dimensionally stable floor covering comprises a tufted textile substrate and a reinforcement layer attached to the textile substrate. The reinforcement layer includes an adhesive backing compound and reinforcement fibers surrounded by the adhesive backing. The fibers may form a continuous layer on the back side of the floor covering or may be dispersed within the adhesive backing compound. The adhesive backing compound may be hot water-soluble to facilitate recycling of the floor covering. The floor covering may optionally include additional backing layers (including cushions) and may be used as a broadloom carpet, a carpet tile, or other modular floor covering products. Methods of manufacturing, installing, and recycling the present floor coverings are also provided.