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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.
Solution
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.
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