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A person starts from a point A and travels 3 km east - wards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the destination is?
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- 12 KM
- 15 KM
- 16 KM
- 18 KM
- None of these
Correct Option: B
Draw the figure of movement with the help of given below direction graph.
A person starts from a point A and travels 3 km East - Wards to B. Then he turns left and travels 9 km to reach C.
He again turns left and travels 15 km and reaches his destination D.
The movements of the person are as shown in Figure
Clearly, AB = 3 km, BC = 3AB = (3 × 3) km = 9 km, CD = 5AB = (5 × 3) km = 15 km,
Draw AE ? CD.
Then, CE = AB = 3 km
AE = BC = 9 km
DE = (CD – CE) = (15 – 3) km = 12 km.
In triangle AED, AD2 = AE2 + DE2
or AD2 = 92 + 122
or AD2 = 81+ 144
or AD2 = 225
or AD2 = 152
AD = 15
Required distance = AD = 15 km
