Question : Directions: Suyash starts walking from his office and walks 40 m towards the south. From there, he turns right and walks 35 m, and then he turns right again and walks 70 m. Finally, he turns right one more time and walks 75 m to reach his home. What is the shortest distance between his office and his home?
Option 1: 40 m
Option 2: 50 m
Option 3: 70 m
Option 4: 85 m
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Correct Answer: 50 m
Solution :
Firstly, we will draw the diagram as per the given instructions –
Now, we have to find the shortest distance between his office and his home.
Here, O is the starting point and D is the finishing point and OD is the total distance from the starting point.
AB = CE = 35m; BC = 70m; CD = 75m
And, OE = AE – AO = 70 – 40 = 30m
And, DE = CD – CE = 75 – 35 = 40m
By applying the Pythagorean theorem –
(DO)
2
= (DE)
2
+ (EO)
2
(DO)
2
= (40)
2
+ (30)
2
= 1600 + 900 = 2500
⇒ DO = $\sqrt2500$ = 50m
So, the shortest distance between his office and his home is 50m. Hence, the second option is correct.
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