Question

The area enclosed by $2|x|+3|y|⩽6$

• A. ) 3 sq. units
• B. 4 sq. units
• C. 12 sq. units
• D. ) 49/12 sq. units

Answer 1

The correct option is C 12 sq. units

Given : $2|x|+3|y|\le 6$

We will have $2x+3y\le 6$, $x\ge 0,y\ge 0$

$2x-3y\le 6$, $x\ge 0,y\le 0$

$-2x+3y\le 6$, $x\le 0,y\ge 0$

$-2x-3y\le 6$, $x\le 0,y\le 0$

$\Rightarrow 2x\pm 3y=6$ & $2x\pm 3y=-6$

This set will denote rhombus

Length of diagonals $=4,6$

Area of rhombus $=\frac{1}{2}\times d_1\times d_2$ (Product of diagonals)

$=\frac{1}{2}\times 4\times 6$

$=12$ sq. units