Question

The length of a room exceeds its breadth by 3 m. If both the length and breadth, are increased by 1m, then the area of the room is increased by 18 cm². Find the length and breadth of the room.

Answer 1

Let the breadth of the rectangle be x m.
Then, the length = (x + 3)m.
Then, Area of the room = x(x + 3)m²
If both the length and breadth, are increased by 1m, then:
Increased length = (x + 4)m.
Increased Breadth = (x + 1)m.
Given, If both the length and breadth, are increased by 1m, then the area of the room is increased by 18cm²
⇒ (x + 1)(x + 4) = x(x + 3) + 18
⇒ (x² + x + 4x + 4) = x² + 3x + 18
⇒ 5x - 3x = 18 - 4 = 14
⇒ 2x = 14
⇒  x = 7cm
Thus, the breadth of the rectangle is 7m.
Then, the length = 10m.