Question

The length of the room exceeds its breadh by 3m. If the length is incresed by 3m and breadth is deacreased by 2m, the area remains the same. Find the length and breadth of the room.

Answer 1

Let the breadth be the x.

length = x + 3m

Area = length * width
A = (x+3m) (x)
A = x² + 3x

Length is increased by 3m and breadth is decreased by 2m, area remains the same.

Length = (x + 3 + 3) ⇒ (x + 6)
Width = (x-2)

x² + 3x = (x + 6)(x-2)
x² + 3x  = x(x-2) +6(x-2)
x² + 3x = x² - 2x + 6x - 12
x² + 3x = x² + 4x - 12
x² - x² + 3x - 4x = -12
-x = -12
x = 12m breadth of the room.

x + 3 = 12 + 3 = 15m length of the room.

Answer 2

Let the length of the room be x meters and he 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) = 12  On substituting y = 12 in (i), we get:  x – 12 = 3  ⇒ x = (3 + 12) = 15  Hence, the length of the room is 15 meters and its breadth is 12 meters.