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 the 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)

y = 12

On substituting y = 12 in (i), we get:

x – 12 = 3

⇒ x = (3 + 12)

⇒ x = 15

Hence, the length of the room is 15 meters and its breadth is 12 meters.