Read the given information carefully and answer the questions given beside: (A…
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Read the given information carefully and answer the questions given beside: (A set of 3 questions)
Lihaan walks 8m towards south from his office to reach a park. Then he takes a left turn and walks 15m to reach a traffic signal. Then he turns 90° anticlockwise and walks 8m to reach a coffee shop. From the coffee shop, he takes a left turn and walks 8m to reach home.
What is the shortest distance between Lihaan's office and the traffic signal?
- A.
30 m
- B.
25 m
- C.
17 m
- D.
15 m
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept: When a path consists of two straight-line segments that meet at a right angle, the direct (straight-line) distance between the path's start point and its end point is the hypotenuse of that right triangle — found using the Pythagorean theorem: hypotenuse = square root of (leg one squared + leg two squared).
Application: Lihaan starts at the office and walks south 8m to the park — this is the first leg of the path. Facing south, a left turn points him east, so he then walks 15m east to the traffic signal — this is the second leg, perpendicular to the first, since south and east are at right angles to each other. So the office and the traffic signal sit at the two ends of the hypotenuse of a right triangle with legs 8m and 15m.
Computing the hypotenuse: 82 + 152 = 64 + 225 = 289. The square root of 289 is 17, so the shortest distance from office to traffic signal is 17m.
Cross-check: 8, 15, 17 is a well-known Pythagorean triple (82 + 152 = 64 + 225 = 289 = 172), which independently confirms the arithmetic.
