Rajesh walks 4 km East from home, then turns right and walks 3 km South. What is his straight-line distance from home?

Introduction / Context:
Two perpendicular moves form the legs of a right triangle. The shortest distance from start to end is the hypotenuse, computed by the Pythagorean theorem.

Given Data / Assumptions:

• 4 km East, then 3 km South.
• We need straight-line distance from home to the endpoint.

Concept / Approach:
Right triangle with legs 4 and 3 has hypotenuse 5 (the well-known 3-4-5 triangle). Units remain in kilometres.

Step-by-Step Solution:

Verification / Alternative check:
Memorized Pythagorean triples (3-4-5) quickly confirm the result without full calculation.

Why Other Options Are Wrong:
Values other than 5 contradict the Pythagorean relation for a right triangle with legs 3 and 4.

Common Pitfalls:
Mistaking 4.5 or 5.5 as plausible averages; the distance must satisfy a^2 + b^2 = d^2.

Final Answer:
5 km.