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.
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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
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