Mathematics
If the length and breadth of a room are increased by 1 metre each, the area is increased by 21 square meters. If the length is decreased by 1 meter and the breadth is increased by 2 meters, the area is increased by 14 square meters. Find the perimeter of the room.
Answer
Let length be x and breadth be y meters.
So, area = xy m2.
According to first condition,
⇒ (x + 1)(y + 1) = xy + 21
⇒ xy + x + y + 1 = xy + 21
⇒ xy - xy + x + y = 21 - 1
⇒ x + y = 20 …….(i)
According to second condition,
⇒ (x - 1)(y + 2) = xy + 14
⇒ xy + 2x - y - 2 = xy + 14
⇒ 2x - y = xy - xy + 14 + 2
⇒ 2x - y = 16 …….(ii)
Adding (i) and (ii) we get,
⇒ x + y + (2x - y) = 20 + 16
⇒ 3x = 36
⇒ x = 12.
Substituting value of x in (i) we get,
⇒ 12 + y = 20
⇒ y = 8.
Perimeter = 2(length + breadth) = 2(x + y) = 2(12 + 8) = 2(20) = 40 meters.
Hence, perimeter of room = 40 meters.
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