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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. units
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D
24 sq. units
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Solution

The correct option is C 12 sq. units
The given inequality is equivalent to the following system of inequalities.
2x+3y6, when x0, y0
2x3y6, when x0, y<0
2x+3y6, when x<0, y0
2x3y6, when x<0, y<0
which represents a rhombus with sides
2x+3y=6,2x+3y=6,2x3y=6 and 2x3y=6
Vertex of rhombus will be (3,0),(3,0),(0,2),(0,2)

Length of the diagonals along xand yaxes is 6 and 4 units respectively,

Therefore, the required area =12×6×4=12 sq. units.

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