Let the breadth of a room = x m
According to the question,
Length of the room = x + 3
Then, Area of room = (x + 3)× (x) m2
= x2 + 3x
Condition II:
Area remains same,
when length = (x + 3 + 3) m = (x + 6) m
and breadth = (x – 2) m
According to the question,
x2 + 3x = (x + 6)(x – 2)
⇒ x2 + 3x = x2 – 2x + 6x – 12
⇒ 3x = 4x – 12
⇒ 3x – 4x = – 12
⇒ x = 12
So, length of the room = (x + 3) = 12 + 3 = 15m
Hence, the length of the room is 15m and the breadth of a room is 12m