Question

a room 5m long and 4m wide is sorrounded by a verandah. if the verandah occupies an area of 22m find the width of the verandah

Answer 1

Given area of varandah = 22 m2( meter sq)
lengh of room = 5m, breadth of room = 4m
 then, Area of room = 5 x 4 m2 = 20 m2
Therefore width of varandah = 22 + 20 = 42 , 42 is factor of 6 and 7, if we add 1 meter in lengh and breadth of room we ll get that so .. width of varandah will be 1 meter.

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Answer 2

Given data : A room 5 m long and 4 m wide is sorrounded by a verandah. The verandah occupies an area of 22 m².

Solution : Assume that the width of the verandah is the same in all directions. Here we take the width of the verandah to be x.

The verandah occupies an area of 22 m². ----{1}

➜ Length of the verandah (with room) = (5 + 2x) m

➜ Breadth of the verandah (with room) = (4 + 2x) m

Now,

➜ Area of the verandah (with room)

= length * breath

➜ Area of the verandah (with room)

= (5 + 2x) * (4 + 2x)

➜ Area of the verandah (with room)

= 20 + 10x + 8x + 4x²

➜ Area of the verandah (with room)

= 4x² + 18x + 20

Now, a/c to given data;

➜ Length of the room = 5 m

➜ Breadth of the room = 4 m

Let, shape of the room be rectangular,

➜ Area of the room = length * breadth

➜ Area of the room = 5 * 4

➜ Area of the room = 20 m²

Here, we know that, (a/c to figure)

➜ Area of the verandah (with room) = Area of the room + Area of the verandah

➜ 4x² + 18x + 20 = 20 + 22 [from {1}]

➜ 4x² + 18x + 20 = 42

➜ 4x² + 18x + 20 - 42 = 0

➜ 4x² + 18x - 22 = 0

Divide eq. by 2

➜ 2x² + 9x - 11 = 0

➜ 2x² + 11x - 2x - 11 = 0

➜ x (2x + 11) - 1 (2x + 11) = 0

➜ (x - 1) (2x + 11) = 0

➜ x - 1 = 0 or 2x + 11 = 0

➜ x = 1 or 2x = - 11

➜ x = 1 or x = - 11/2

Here, we know, width of the verandah is never negative. Hence, x ≠ - 11/2 and x = 1

Answer : Hence, the width of the verandah is 1 m.