Question : Directions: A man starts the journey from home. He goes 5 km to the north, then proceeds 10 km to the right. From there he again turns right and goes 10 km. How far is he from home?
Option 1: $\sqrt{200}$
Option 2: $\sqrt{150}$
Option 3: $\sqrt{225}$
Option 4: $\sqrt{125}$
Correct Answer: $\sqrt{125}$
Solution : Firstly, we will draw the diagram as per the given instructions –
In the above figure, A is the starting point and E is the finishing point of the man.
AE is the distance between the man and his home.
Here, BC = AD = 10 km; AB = DC = 5 km; DE = 10 – 5 = 5 km
By applying the Pythagoras theorem –
(AE)
2
= (AD)
2
+ (DE)
2
(AE)
2
= (10)
2
+ (5)
2
(AE)
2
= 100 + 25
⇒ AE = $\sqrt{125}$ km
So, the distance between the man and his home is $\sqrt{125}$ km . Hence, the fourth option is correct.
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