Question

A room 5 m long and 4 m wide is surrounded by a verandah. If the verandah occupies an area of 22 m², find the width of the varandah.

Answer 1

Let the width of the verandah be x m.
Length of the room AB = 5 m and BC = 4 m

∴ Area of the room = 5 m x 4 m = 20 m²
Length of the verandah PQ = (5 + x + x) = (5 + 2x) m
Breadth of the verandah QR = ( 4 + x + x) = (4 + 2x) m
Area of verandah PQRS = (5 + 2x) x (4 + 2x) = (4x² + 18x + 20 ) m²
∴ Area of verandah = Area of PQRS − Area of ABCD
⇒ 22 = 4x² + 18x + 20 − 20
⇒ 22 = 4x² + 18x
⇒ 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 = $-\frac{11}{2}$
The width cannot be a negative value.
So, width of the verandah = x = 1 m.