The region represented by

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Question:

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

  1. (1) square of side length $2 \sqrt{2}$ units

  2. (2) rhombus of side length 2 units

  3. (c) square of area $16 \mathrm{sq}$. units

  4. (4) rhombus of area $8 \sqrt{2}$ sq. units

Correct Option: 1

Solution:

Let, $\mathrm{C}_{1}:|y-x| \leq 2$

$\mathrm{C}_{2}:|y+x| \leq 2$

By the diagram, region is square

Now, length of side $=\sqrt{2^{2}+2^{2}}=2 \sqrt{2}$

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