Question

The region represented by $|x-y|\le 2$ and $|x+y|\le 2$ is bounded by a:

• A. Square of side length $2\sqrt{2}$ units
• B. Rhombus of side length $2$ units
• C. Square of area $16sq$ units
• D. Rhombus of area $8\sqrt{2}sq.$ units

Answer 1

The correct option is A Square of side length $2\sqrt{2}$ units

$|x-y|\le 2$ and $|x+y|\le 2$

$\Rightarrow x-y\le 2$ or $x-y\ge 2$ and $x+y\le 2$ and $x+y\ge -2$

After plotting them on the graph the common region is

Square whose side is $2\sqrt{2}$