A policeman stepped out of the police station and walked 60 m towards west. He then took a left turn 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?
A policeman stepped out of the police station and walked 60 m towards west. He then took a left turn 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? Correct Answer 142 m
Representing the given information on NESW diagram:
[ alt="F1 Shraddha Prashant 11.03 (28)" src="//storage.googleapis.com/tb-img/production/21/03/F1_Shraddha_Prashant_11.03%20%2828%29.png" style="width: 443px; height: 390px;">
The approximate shortest distance between the police station and the restaurant via the fruit shop is:
Distance = OB + DB
But Here, OB = DB
Then, Distance = 2(OB) → (i)
Applying Pythagoras theorem in ∆OAB :
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
(OB)2 = (AB)2 + (OA)2
(OB)2 = (38)2 + (60)2
(OB)2 = 1444 + 3600 = 5044
OB = √5044 = 71.02
Putting the value of OB in equation (i),
Distance = 2(OB) → 2 × 71.02 → 142.4 (approx. 142)
Hence, the correct answer is "142 m".
