Question

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

Answer 1

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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.