Question

A romm of length 5 m and breadth 4 m has a varandah all around it,
of area 22 sqm. Find the width of varandah

Answer 1

Answer:

width = 2 m

Step-by-step explanation:

area of room = 5 × 4 = 20

length with veranda = 5 + x

breadth with veranda = 4 + x

area of room with veranda = (5 + x) (4 + x)

area of veranda = 22 m

$(x + 5)(x + 4) \\ = {x}^{2} + 9x + 20 \\ \\ ({x}^{2} + 9x + 20) - 20 = 22 \\ {x}^{2} + 9x - 22 = 0 \\ {x}^{2} - 2x + 11x - 22 = 0 \\ x(x - 2) + 11(x - 2) = 0 \\ (x - 2)(x + 11) = 0 \\ x = 2 \: \: \: \: x = - 11$

as width cannot be negative

x = 2

width of the veranda is 2 mts