Dilip walks 60 m south from his house. Then he turns left and walks 80 m. He again turns left and walks 90 m. Finally, he turns left and walks 120 m to reach a garden.

What is the shortest distance between his house and the garden?

1. A

   80 m

2. B

   70 m

3. C

   55 m

4. D

   50 m

Appeared in: NVS Staff Nurse - 2022

Explanation

• The problem is solved by breaking down the movements into perpendicular components (North-South and East-West).
• The net displacement is 30 m North and 40 m West from the starting point.
• The shortest distance is the hypotenuse of the right-angled triangle formed by these two displacements.
• Using the Pythagorean theorem (a² + b² = c²), the distance is calculated as √(30² + 40²) = √(900 + 1600) = √2500 = 50 m.

Why Other Options Were Wrong

• Option A: 80 m is the distance of the second leg of the journey (Eastward movement). It does not represent the final shortest distance from the start.
• Option B: 70 m is the arithmetic sum of the two net displacements (30 m + 40 m). The shortest distance is the hypotenuse, not the sum of the sides.
• Option C: 55 m is a calculation error. It does not result from the correct application of the Pythagorean theorem with sides 30 and 40.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the shortest distance between two points after a series of movements using the Pythagorean theorem as background academic context rather than a clinical decision trigger.
• This question type is not directly related to clinical nursing practice but is included in nursing entrance and recruitment exams to assess logical reasoning and problem-solving skills.
• These skills are crucial for nurses in situations requiring critical thinking, such as prioritizing care, troubleshooting equipment, or navigating complex hospital layouts.
• What if the final turn was 180 degrees (turning back) instead of a left turn? The person would move 120 m back East from (80, 30), ending at (200, 30). The shortest distance would then be √(200² + 30²) = √40900 ≈ 202.2 m.

How to Approach the Question

• First, visualize the path of movement. It's helpful to draw a simple diagram with North, South, East, and West directions.
• Break down each movement into its North-South and East-West components. Remember that turning left from South is East, from East is North, and from North is West.
• Calculate the net displacement in the North-South direction by adding all North movements and subtracting all South movements.
• Similarly, calculate the net displacement in the East-West direction by adding all East movements and subtracting all West movements.
• These two net displacements form the perpendicular sides of a right-angled triangle.
• Use the Pythagorean theorem (a² + b² = c²) to calculate the length of the hypotenuse, which represents the shortest distance from the start to the end point.

Concept Tested & Keywords

• Concept Tested: Calculating the shortest distance between two points after a series of movements using the Pythagorean theorem.
• Stem keywords: walks, south, turns left, east, north, west, shortest distance
• Lead-in keywords: shortest distance
• Negative lead-in flag: false

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QWN6ieXLK-iEobRLet9X37

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