Question

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

• A. 3 sq units
• B. 4 sq units
• C. 12 sq unit
• D. 24 sq units

Answer 1

The correct option is C

12 sq unit

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

$\therefore$ Length of the diagonals is 6 nd 4 units along x - axis and y - axis
$\therefore$ The required area $=\frac{1}{2}\times 6\times 4=12squnits$