question_answer

A villager visited in many villages to invite his relatives on his son's marriage from his village Rampur. He went to Kohinoor, the village of his son-in-law, 4 km away in South-East direction of Rampur. From there he went to Kishangarh, the village of his brother-in-law, 3 km away in South of Kohinoor. He then went to Ujalapur, the village of his friend, \[2\sqrt{2}\] km away in west of Kishangarh. How far was Rampur from Ujalapur?

A)  \[(3+2\sqrt{2})\]km      

B)  \[(3-2\sqrt{2})\] km       

C)  \[(4+2\sqrt{2})\] km     

D)  \[(4-2\sqrt{2})\] km

Correct Answer: A

Solution :

:                                   In \[\Delta OAB,\text{ }{{\left( OA \right)}^{2}}+{{\left( AB \right)}^{2}}={{\left( OB \right)}^{2}}\] \[{{\left( OA \right)}^{2}}=16-8=8\] \[OA=2\sqrt{2}\]km Required distance =OC=OA+AC       \[=2\sqrt{2}+3\]km