Question

A Verandah of area 90 m² is around a room of length 15 m and breadth 12 m. The width of the Verandah is​

Answer 1

Now

(15+2x)(12+2x)-(15)(12)=90

$\bold{ \large{4 {x}^{2} + 54x = 90}} \\ \\ \bold{ \large{2 {x}^{2} + 27x - 45 = 0}} \\ \\ \bold{ \large{2 {x}^{2} + 30x - 3x - 45 = 0}} \\ \\ \bold{ \large{2x(x + 15) - 3(x + 15) = 0}} \\ \\ \bold{ \large{(2x - 3)(x +15) = 0}} \\ \\ \bold{ \large{x \neq -15 \: as \: it \: doesnt \: satisfy \: the \: first \: equation}} \\ \\ \bold{ \large{ = > x = 1.5m}}$

Therefore the width of the veranda is 1.5 m.

hope it helps.