Question

The length of a room exceeds its breadth by 3 meters. If the length is increased by 3 meters and the breadth is decreased by 2 meters, the area remains the same. Find the length and the breadth of the room.

Answer 1

Let the length of the room be x meters and he breadth of the room be y meters.
Then, we have:
Area of the room = xy
According to the question, we have:
x = y + 3

⇒ x – y = 3                                       …….(i)
And, (x + 3) (y – 2) = xy
⇒ xy – 2x + 3y – 6 = xy
⇒ 3y – 2x = 6                               ……..(ii)
On multiplying (i) by 2, we get:
2x – 2y = 6                                  ……….(iii)
On adding (ii) and (iii), we get:
y = (6 + 6) = 12
On substituting y = 12 in (i), we get:
x – 12 = 3
⇒ x = (3 + 12) = 15
Hence, the length of the room is 15 meters and its breadth is 12 meters.