Regretting Room Rearrangement?

Robert the giant has a new bed, which he wishes to fit into his bedroom. There is no other furniture in the room and the room measures 5m by an arbitrarily long distance as shown in the diagram. The bed enters the room as shown below and Robert can not lift the bed at an angle, only rotate, to ideally place the bed in the pink area below (vertical). The bed he bought has a width of 2m and a length which was the longest possible bed he could get, so that it would rotate and fit by his far wall, given that the beds that are sold have an increment of 0.1m (e.g. 1.2m, 1.3m, 1.4m).

What is the length of Robert's bed in metres? Give your answer to 1 decimal place, even if it is an integer, e.g. "1.0"