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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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