Question

The length of a room exceeds its breadth by 2 meters. If the length be increased by 4 meters and the breadth decreased by 2 meters, the area remains the same. Find the surface area of its walls if the height is 3 meters.

Answer 1

Length of room = 9 m and breadth of room= 6 m

Step-by-step explanation:

Let the breadth be =  x.

Length = x + 2 m

Area of room = length x  width

A = (x+2m) (x)

A = x² + 2x

• Length increases by 4 m and breadth decreases by 2 m, therefore area remains the same.

Length = (x + 2+ 4) 

           ⇒ (x + 6)

Width = (x-2)

• Breadth of the room

x² + 2x = (x + 6)(x-2)

x² + 2x  = x(x-2) +6(x-2)

x² + 2x = x² - 2x + 6x - 12

x² + 2x = x² + 4x - 12

x² - x² + 2x - 4x = -12

-2x = -12

x = 6 m

• Length of the room

x + 3 = 6 + 3 = 9 m

Surface area of the wall = length x breadth = x^2 +2x