Question

The length of a room exceeds its breadth by 3 metres.If the lengths increased by 3 metres and the breadth is decreased by 2 metres,the area remains the same.Find the length and the 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.