A tourist has strayed from his path while on his way to his hotel. He moves…
2024
A tourist has strayed from his path while on his way to his hotel. He moves 28km towards south, then he moves 20km towards west, then 4km north and then 2km towards east to reach his hotel. What is the distance of shortest possible route?
- A.
45 km
- B.
20km
- C.
18km
- D.
30km
Show answer & explanation
Correct answer: D
Concept: When movement happens along two perpendicular directions (north-south and east-west), the net displacement between the start and end points equals the hypotenuse of a right triangle whose legs are the net north-south displacement and the net east-west displacement — found using the Pythagorean theorem, hypotenuse = √(a2 + b2).
The tourist walks 28 km south, then 20 km west, then 4 km north, then 2 km east.
Net north-south displacement = 28 km south − 4 km north = 24 km south.
Net east-west displacement = 20 km west − 2 km east = 18 km west.
These two net displacements are perpendicular to each other, forming the two legs of a right triangle whose hypotenuse is the shortest route to the hotel.
Shortest distance = √(242 + 182) = √(576 + 324) = √900 = 30 km.
Cross-check: 24, 18, 30 form a scaled Pythagorean triple — six times the standard 3-4-5 triple (6×4 = 24, 6×3 = 18, 6×5 = 30) — which independently confirms the computed hypotenuse of 30 km.