Question

A room 5m long and 4 m wide is surrounded by a verandah. If the verandah occupies an area of 22 m square , find the width of the verndah a b c d e F e f Db-

Answer 1

let the width of the veranda be x

of the room with Veranda :-
length = 5 + 2x
breadth = 4 + 2x
area = (5 + 2x)(4 + 2x)
= 20 + 10x + 8x + 4x^2
= 4x^2 + 18x + 20

Now area of veranda
= area of the room with Veranda
- area of room without veranda
22 = 4x^2 + 18x + 20 - 20
4x^2 + 18x = 22
2x^2 + 9x -11 = 0
2x^2 + 11x -2x - 11 = 0
x(2x + 11) - (2x + 11) =0
(x - 1)((2x + 11) = 0
therefore
x=1
the width of the veranda = 1m