KöMaL 2020 K658

In each of two rectangular rooms of the same floor area, the floor is covered with $25~\mathrm{cm}\times40~\mathrm{cm}$ tiles. No tile is cut. In one room, the 40-cm sides of the tiles are parallel to the longer side of the rectangle, and in the other room they are parallel to the shorter side. In one room, there are 9 fewer tiles along the longer wall than in the other room, and 6 more tiles along the shorter wall than in the other. How long are the sides of the bases of the rooms?