Rajesh walks 4 km East from home, then turns right and walks 3 km South. What is his straight-line distance from home?
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A4 km.
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B5 km.
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C5. 5 km.
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D4.5 km.
Answer
Correct Answer: 5 km.
Explanation
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:
Let legs be a = 4, b = 3.Distance d = sqrt(a^2 + b^2) = sqrt(16 + 9) = sqrt(25) = 5.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.