Question : Directions: A policeman stepped out of the police station and walked 60 m towards the west. He then took a left tum and walked 38 m to reach a fruit shop. He then took a right turn and walked 60 m. He then took a right turn and walked 38 m to reach a restaurant. What is the approximate shortest distance between the police station and the restaurant via the fruit shop?
Option 1: 71 m
Option 2: 150 m
Option 3: 112 m
Option 4: 142 m
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Correct Answer: 142 m
Solution : Firstly, we will draw the diagram as per the given instructions –
Now, we have to find the shortest distance between the police station and the restaurant via the fruit shop
The approximate shortest distance between the police station and the restaurant via the fruit shop is OB + DB.
Here, OB = DB
Therefore, Distance = 2(OB)
Using the Pythagoras, we get –
(OB)
2
= (AB)
2
+ (OA)
2
(OB)
2
= (60)
2
+ (38)
2
(OB)
2
= 3600 + 1444
(OB)
2
= 5044
OB = 71.02
Now, on putting the value of OB, we get –
Distance = 2(OB) = 2 × 71.02 = 142.04 (approximately 142)
The approximate shortest distance between the police station and the restaurant via the fruit shop is 142m. Hence, the fourth option is correct.
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