Question

A room 5 m long and 4 m wide is surrounded by a verandah. If the verandah
occupies an area of 22 m^2, find the width of the verandah.
Let ABCD be the room surrounded by a verandah.
Let the width of verandah be x m.
Length of the room = 5 m, breadth of the room = 4 m.
Exm
Area of the room ABCD = (5x4) m^2 = 20 m^2.
Let EFGH be the region consisting of room and verandah.
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Answer 1

Answer:

Let the width of the verandah be x m.

Length of the room AB = 5 m and BC = 4 m

Step-by-step explanation:

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 = 

The width cannot be a negative value.

So, width of the verandah = x = 1 m.