Percentage error in area from side measurement errors In measuring a rectangle, one side is taken 5% in excess and the other side 4% in deficit. Find the percentage error in the computed area.

Introduction / Context:Area of a rectangle is the product of its length and breadth. When each dimension has a percentage error, the approximate percentage error in the product equals the product of the error factors minus one.

Given Data / Assumptions:

• First side taken as 105% of true ⇒ factor 1.05
• Second side taken as 96% of true ⇒ factor 0.96

Concept / Approach:Computed area factor = 1.05 * 0.96. Percentage error = (Computed factor − 1) * 100%.

Step-by-Step Solution:

Verification / Alternative check:Using small-error approximation: +5% and −4% roughly add to about +1%, but the exact multiplicative method yields +0.8%, which is precise.

Why Other Options Are Wrong:0.7%, 0.9%, and 0.3% are near misses that arise from additive or rounding approximations rather than correct multiplication of error factors.

Common Pitfalls:Simply adding +5% and −4% gives +1% which is not exact; products of measurements require multiplicative treatment.

Final Answer:0.8%