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Difficulty: EasyDirection and Distance Test

An inspector starts walking from a police station and walks 30 m30\text{ m} towards the East. He then turns right and walks 40 m40\text{ m} to reach a checkpoint. What is the shortest direct distance between the police station and the checkpoint?

  1. 50 m50\text{ m}Answer
  2. B
    70 m70\text{ m}
  3. C
    10 m10\text{ m}
  4. D
    107 m10\sqrt{7}\text{ m}

Answer

The shortest direct distance between the police station and the checkpoint is 50 m50\text{ m}.
The inspector's path consists of 30 m30\text{ m} East followed by a perpendicular 40 m40\text{ m} South. The shortest direct path forms the hypotenuse of a right-angled triangle with legs of 30 m30\text{ m} and 40 m40\text{ m}. Applying 302+402=2500\sqrt{30^2 + 40^2} = \sqrt{2500} gives 50 m50\text{ m}.

Step-by-Step Solution

1
Determine the path and orientations.
The inspector moves 30 m30\text{ m} East and then turns right to walk 40 m40\text{ m} South.
A right turn when traveling East directs movement towards the South.
2
Calculate the shortest straight-line distance using the Pythagorean theorem.
Distance d=302+402=900+1600=2500=50 md = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500} = 50\text{ m}.
The East and South movements are perpendicular to each other, forming a right-angled triangle where the direct distance is the hypotenuse.

Key Concept

Shortest Distance using Pythagorean Theorem
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Topics

Direction and Distance Test

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