From a square (side s), a rectangle is formed by increasing “length” by 40% and “breadth” by 30%. By what percentage does the new rectangle’s area exceed the original square’s area?

Introduction / Context:
Area scale factors multiply. If a dimension is scaled by a% and the other by b%, the area is scaled by (1 + a) * (1 + b) (using decimal form). Comparing this to the original square area s^2 gives the percentage increase directly.

Given Data / Assumptions:

• Original square side = s ⇒ area = s^2
• New rectangle dimensions: 1.4s and 1.3s

Concept / Approach:
New area = (1.4s) * (1.3s) = 1.82 s^2. Therefore, percentage increase = (1.82 − 1) * 100% = 82%.

Step-by-Step Solution:
Area factor = 1.4 * 1.3 = 1.82% increase = (1.82 − 1) * 100% = 82%

Verification / Alternative check:
Check with sample s = 10: original area = 100; new = 14 * 13 = 182; increase = 82 on 100 = 82% — consistent.

Why Other Options Are Wrong:
42% and 62% arise from incorrect additive reasoning (40% + 30% or partial products). “None of these” is unnecessary since 82% fits exactly.

Common Pitfalls:
Adding 40% and 30% (getting 70%) instead of multiplying scale factors; area scales with the product of linear scalings, not their sum.

Final Answer:
82%