Error propagation – Side measured 2% in excess for a square: If the side of a square is measured 2% too high, what is the percentage error in the computed area?
Aptitude
Area
Difficulty: Easy
Choose an option
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A1.04
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B2.04
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C3.04
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D4.04
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ENone of these
Answer
Correct Answer: 4.04
Explanation
Introduction / Context:When a quantity depends on the square of a measurement, a small percentage error in the measurement approximately doubles in the result; exactly, the factor is squared.
Given Data / Assumptions:
- Side measured = 1.02 * true side.
- Area ∝ side^2.
Concept / Approach:Compute exact factor: (1.02)^2 = 1.0404 ⇒ area error = +4.04%.
Step-by-Step Solution:
Let true side = s; measured side = 1.02s.True area = s^2; measured area = (1.02s)^2 = 1.0404 s^2.Percentage error = (1.0404 − 1) × 100% = 4.04%.Verification / Alternative check:Approximation 2*(2%) = 4% is close; exact is 4.04%.
Why Other Options Are Wrong:1.04, 2.04, 3.04 misapply linear approximation or mis-square 1.02.
Common Pitfalls:Using linear instead of squaring; misinterpreting percentage vs decimal.
Final Answer:4.04