Let the width of the verandah be x m.
Given Length of the room AB = 5 m and breadth of the room, BC = 4 m
We know that area of rectangle = length x breadth
Area of the room = 5 m x 4 m
= 20 m2
From the figure, it is clear that
Length of the veranda PQ = (5 + x + x) = (5 + 2x) m
Breadth of the veranda QR = (4 + x + x) = (4 + 2x) m
Area of veranda PQRS = (5 + 2x) x (4 + 2x)
= (4×2 + 18x + 20) m2
Area of veranda = Area of PQRS – Area of ABCD
22 = 4x2 + 18x + 20 – 20
22 = 4x2 + 18x
On dividing above equation by 2 we get,
11 = 2x2 + 9x
2x2 + 9x – 11 = 0
2x2 + 11x – 2x – 11 = 0
x (2x+11) – 1 (2x+11) = 0
(x- 1) (2x+11)= 0
When x – 1 = 0, x = 1
When 2x + 11 = 0, x = (-11/2)
The width cannot be a negative value. So, width of the veranda = x = 1 m