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Question

The area enclosed by 2|x| + 3|y| 6 is


A

3 sq units

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B

4 sq units

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C

12 sq unit

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D

24 sq units

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Solution

The correct option is C

12 sq unit


The given inequality is equivalent to the following system of inequalities.
2x + 3y 6, when x 0, y 0
2x - 3y 6, when x 0, y 0
- 2x + 3y 6, when x 0, y 0
- 2x - 3y 6, when x 0, y 0
Combining these inequalities represents a rhombus with sides 2x±3y=6 and 2x±3y=6

Length of the diagonals is 6 nd 4 units along x - axis and y - axis
The required area =12×6×4=12 sq units


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