Read the given information carefully and answer the questions given below (a…
2024
Read the given information carefully and answer the questions given below (a set of 3 questions): Lihaan walks 8 m south from his office to reach a park. He then turns left and walks 15 m to reach a traffic signal. He then turns 90 degrees anticlockwise and walks 8 m to reach a coffee shop. From the coffee shop, he turns left and walks 8 m to reach home. What is the shortest distance between Lihaan's office and the traffic signal? [Questions 3 to 5 are linked together.]
- A.
30 m
- B.
25 m
- C.
17 m
- D.
15 m
Show answer & explanation
Correct answer: C
In direction-and-distance problems, a person's path can be broken into straight legs along the cardinal directions. When two consecutive legs are perpendicular to each other, the straight-line (shortest) distance between their end points is the hypotenuse of the right triangle they form, given by the Pythagorean theorem: hypotenuse squared equals the sum of the squares of the two legs.
From the office, Lihaan walks 8 m due south to reach the park.
At the park he is facing south; taking a left turn there points him east, and he walks 15 m east to reach the traffic signal.
So, relative to the office, the traffic signal lies 8 m south and 15 m east of it -- two legs at right angles to each other, forming a right triangle with the office-to-signal line as its hypotenuse.
Applying the Pythagorean theorem: distance = √(82 + 152) = √(64 + 225) = √289 = 17 m.
This can be cross-checked independently: 8, 15, 17 is a well-known Pythagorean triple, since 82 + 152 = 289, which equals 172. So the shortest distance between the office and the traffic signal is 17 m.
