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Rajbir Singh, a farmer, wants to build an extension at the rear of his house. Planning regulation states that the area of the extension must be 40% of the area of the original house. The dimension of the original house is 12 meters by 10 meters. An architect also advises that the extension should have its length 2 meters more than its width.
Find the area of the extension.

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58 m

2

48 m

2

68 m

2

78 m

2

answer is B.

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Detailed Solution

Given,
The dimensions of the original house are 12 meters and 10 meters.
Area

= 12 × 10

⇒ 120

2

The extension will be rectangular in shape.
The area of a rectangular field of length and breadth

x

and

y

respectively.
Area

= x × y

New Dimensions,
Let the length and width be

x + 2

and

x

.
Then area of the extension,

x × (x + 2) = 40

% of area of original field

⇒ x 2 + 2 x = 40100 × 120

⇒ x 2 + 2 x − 48 = 0

⇒ x 2 + 8 x − 6 x − 48 = 0

⇒ x (x + 8) − 6 (x + 8) = 0

⇒ (x − 6) (x + 8) = 0

⇒

x = 6

x = − 8

But

x

cannot be negative, so we consider x = 6,
So, x+2 is

⇒

6+2

⇒

8 meters
Length =8m, breadth = 6m.
The area of the extension,
Area

= l × b

⇒ 8 × 6

⇒ 48

2

Thus, the area of the extension is 48 m2.
Therefore, the correct option is 2.

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