A room 5 m long and 4 m wide is surrounded by a verandah. If the veran

1.	A room 5 m long and 4 m wide is surrounded by a verandah. If the verandah occupies an areaof 22 m². find the width of the varandah.
Answer» ANSWER: 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 = The width cannot be a negative value. So, width of the verandah = x = 1 m.

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

Answer»

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 =

The width cannot be a negative value.

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