Question

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

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

Answer 1

The correct option is C $12$ sq. units

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 $x\ge 0,y<0$
$-2x+3y\le 6$, when $x<0,y\ge 0$
$-2x-3y\le 6$, when $x<0,y<0$
which represents a rhombus with sides
$2x+3y=6,-2x+3y=6,2x-3y=6$ and $-2x-3y=6$
Vertex of rhombus will be $(3,0),(-3,0),(0,2),(0,-2)$

Length of the diagonals along $x-$and $y-$axes is $6$ and $4$ units respectively,

Therefore, the required area $=\frac{1}{2}\times 6\times 4=12$ sq. units.