Question

A man walks 24 km distance straight from a place X and reach another place Y in the Eastern direction. At Y, he turns 90 degrees and walks straight towards North to reach the Place Z which is 7 km from Y. The distance between X and Z is

• A. 25 km
• B. 27 km
• C. 37 km
• D. 31 km

Hint:

Use the Pythagoras theorem to find distances in right-angled paths involving east and north directions.

Answer 1

The Correct Option is A

Step 1: Visualizing the path
The man walks 24 km east from X to Y.
From Y, he walks 7 km north to Z.
Step 2: Identify the triangle
The journey from X to Z forms a right-angled triangle with legs: - \(XY = 24\) km (east direction)
- \(YZ = 7\) km (north direction)
Step 3: Find the direct distance (hypotenuse)
Distance \(XZ\) is the hypotenuse: \[ XZ = \sqrt{XY^2 + YZ^2} = \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \text{ km}. \]
Step 4: Conclusion
The straight-line distance between X and Z is 25 km.