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?

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:

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