Length of room, l = 3x + 1 ft.
Breadth of room, b = x² -1 ft.
Now, it is given that university wants each room to have 195 ft² of living space.
So,

So, above equation has two complex root and one real root i.e x = 4.08 ft .
Therefore, Length of room is 13.24 ft and breadth is 15.65 ft.
Hence, this is the required solution.