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

Options

A. 3
B. 12
C. 9
D. 24

Answer

B

Explanation

We have, `2|x| + 3|y| le 6`. This is equivalent to the following system of inequations:
`2x + 3y le 6,` when `x ge 0, y ge 0`
`2x - 3y le 6`, when `x ge 0, y ge 0`
`-2x + 3y le 6`,when`x le 0, y ge 0`
and `-2x- 3y le 6`, when `x le 0,y le 0`.
These inequations form a rhombus having its diagonals of
lenght 6 and 4 units, along the coordinate axes.
So, required area `=(1)/(2) (6 xx 4) = 12` sq. units