Question

A room has a length of 5 m and width of 4 m. It has been surrounded by a verandah. If the verandah has an area of $\bf 22 m^{2}$. $\bf Find \: the \: width \: of \: the \: verandah$

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Answer 1

Answer:

Width of veranda is 1 m

Explanation:

Let the width of the verandah be x m

Given:

Length of the room = 5 m

Breadth of the room = 4 m

Solution:

area of rectangle = length x breadth

Area of the room = 5 x 4 = 20 m²

From the figure,

Length of the veranda PQ = (5 + x + x) = (5 + 2x)

Breadth of the veranda QR = (4 + x + x) = (4 + 2x)

Area of veranda PQRS = (5 + 2x) x (4 + 2x)

= (4x² + 18x + 20) m²

Area of veranda = Area of PQRS – Area of ABCD 22 = 4x² + 18x + 20 – 20

22 = 4x2 + 18x

On dividing above equation by 2,

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 = (-11/2)

The width cannot be a negative value. So, width of the veranda is x = 1 m