John walked 10 meters towards the South. He then turned to his left and walked…
John walked 10 meters towards the South. He then turned to his left and walked 15 meters. What is the shortest distance between his starting point and his current location?
Answer: C. 18 meters — When someone moves along two directions that are perpendicular to each other, the straight-line (shortest) distance between the start and end points is not…
- A.
10 meters
- B.
15 meters
- C.
18 meters
- D.
25 meters
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Correct answer: C
When someone moves along two directions that are perpendicular to each other, the straight-line (shortest) distance between the start and end points is not the sum of the two legs walked — it is the hypotenuse of the right triangle the two legs form, found using the Pythagorean theorem: hypotenuse = square root of (leg one squared + leg two squared).
John first walks 10 meters towards the South — this is the first leg of the path.
Facing South, a left turn points him towards the East, so the second leg is a 15 meter walk towards the East.
South and East are perpendicular directions, so the two legs meet at a right angle at the point where John turned.
The straight-line distance from the starting point to John's final location is therefore the hypotenuse of a right triangle with legs 10 meters and 15 meters.
By the Pythagorean theorem, hypotenuse = √(102 + 152) = √(100 + 225) = √325 ≈ 18.03 meters, which rounds to the closest offered value of 18 meters.
Cross-check: √324 = 18 and √361 = 19, so √325 must lie just above 18 — confirming 18 meters as the closest value. Also, 18 meters is less than the sum of the two legs (10 + 15 = 25 meters), exactly as expected when two legs are perpendicular — the straight-line distance is always shorter than the path actually walked.