A) \[\text{2}\sqrt{5}\,\text{sq}.\]units
B) \[\sqrt{10}\,\text{sq}.\] units
C) \[2\sqrt{10}\,\text{sq}.\] units
D) \[10\,\text{sq}.\] units
Correct Answer: D
Solution :
| Distance between Sonu and Monu |
| \[=\sqrt{{{(5-2)}^{2}}+{{(2-3)}^{2}}}=\sqrt{9+1}=\sqrt{10}\]unit |
| Distance between Monu and Goru |
| \[=\sqrt{{{(5-6)}^{2}}+{{(2-5)}^{2}}}=\sqrt{1+9}=\sqrt{10}\] unit |
| Distance between Goru and Golu |
| \[=\sqrt{{{(3-6)}^{2}}+{{(6-5)}^{2}}}=\sqrt{9+1}=\sqrt{10}\] unit |
| Distance between Golu and Sonu |
| \[=\sqrt{{{(2-3)}^{2}}+{{(3-6)}^{2}}}=\sqrt{1+9}=\sqrt{10}\] unit |
| Distance between -Sonu and Goru |
| \[=\sqrt{{{(2-6)}^{2}}+{{(3-5)}^{2}}}=\sqrt{16+4}\] |
| \[=\sqrt{20}=2\sqrt{5}\]unit |
| Clearly, the distance between all fours are same an diagonally equal, If all four seats connected with a rope, forms a square with equal length, i.e., \[2\sqrt{5}\] units of diagonals |
| \[\therefore \] Area covered by Sonu and its members |
| \[={{(\sqrt{10})}^{2}}=10\,sq.\] units |
| So, option [d] is correct. |
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