Mathematics
The length of a room exceeds its breadth by 3 meters. If the length is increased by 3 m and breadth is decreased by 2 meters, the area remains the same. Find the length and breadth of the room.
Answer
Let x meters be the length of a room and y meters be the breadth of the room.
Given,
The length of a room exceeds its breadth by 3 m,
⇒ x = y + 3 ….(1)
Given,
If length is increased by 3 and breadth decreased by 2, area remains the same,
⇒ (x + 3)(y - 2) = xy
⇒ (xy - 2x + 3y - 6) = xy
⇒ xy - xy = 2x - 3y + 6
⇒ 2x - 3y + 6 = 0 ….(2)
Substituting value of x from equation (1) in (2), we get :
⇒ 2(y + 3) - 3y + 6 = 0
⇒ 2y + 6 - 3y + 6 = 0
⇒ -y + 12 = 0
⇒ y = 12.
Substituting value of y in equation (1), we get :
⇒ x = y + 3
⇒ x = 12 + 3
⇒ x = 15.
Hence, length and breadth of the room are 15 m and 12 m respectively.
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