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The area enclosed by 2|x|+3|y|lt=6 is (...

The area enclosed by `2|x|+3|y|lt=6` is (a) 3 sq. units (b) 4 sq. units 12 sq. units (d) 24 sq. units

A

3 sq. units

B

4 sq. units

C

12 sq. units

D

24 sq. units

Text Solution

Verified by Experts

The correct Answer is:
C
The given inequality is equivalent to the following system of inequalities.
`2x+3y le 6, "when " x ge 0, y ge0`
`2x-3y le 6, "when " x ge 0, y le0`
`-2x+3y le 6, "when " x le 0, y ge0`
`-2x-3y le 6, "when " x le 0, y le0`
which represents a rhombus with sides
`2x+-3y = 6 " and " 2x+- 3y=-6`
The lengths of the diagonals are 6 units and 4 units, respectively, along the x- and y-axes. Therefore, the required area is `1//2 xx 6 xx 4=12` sq. units.
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