Area change with scaled sides of a rectangle\nThe length and breadth of a rectangle increase by 40% and 70%, respectively. By what percentage does the area increase?

Introduction / Context:
Area scales multiplicatively with each dimension. Percent increases become factors (1 + r). Multiply the factors to get the new area factor, then convert back to a percent increase over the original.

Given Data / Assumptions:

• Length factor = 1.40 (40% increase)
• Breadth factor = 1.70 (70% increase)

Concept / Approach:
New area factor = 1.40 * 1.70 = 2.38. Percentage increase = (2.38 − 1) * 100% = 138% over the original area.

Step-by-Step Solution:

Verification / Alternative check:
Pick a = 10 by 10 ⇒ area 100. New sides 14 and 17 ⇒ area 238 ⇒ increase 138%, confirming the factor method.

Why Other Options Are Wrong:
118, 110, and 128 arise from additive or partial scaling errors rather than multiplicative scaling.

Common Pitfalls:
Adding 40% and 70% to get 110% is incorrect because area depends on both dimensions multiplicatively.

Final Answer:
138