A floating platform possesses a rectangular base with dimensions of 4 m by 8 m and a 1.5 cm thickness, made from a material with a density of 8100 kg/m³. The platform is enclosed by walls constructed from platinum, having a 0.32 cm thickness. Find the lowest height necessary for these walls to ensure the platform remains afloat in the lake. The density of water is approximately 1000 kg/m³.