Perimeter change after scaling rectangle sides\nIn a rectangle, length is three times the breadth. If the length and breadth are increased by 30% and 100% respectively, by what percentage does the perimeter increase?

Introduction / Context:
Scaling linear dimensions affects perimeter linearly. Given a fixed relation between length and breadth, we can express the perimeter in terms of one variable and compare before/after values.

Given Data / Assumptions:

• Let breadth = x, length = 3x
• Original perimeter P = 2(3x + x) = 8x
• New length = 1.3 * 3x = 3.9x
• New breadth = 2x

Concept / Approach:
Perimeter scales with the sum of side lengths; compute the new perimeter and compare to the original.

Step-by-Step Solution:

Verification / Alternative check:
Pick x = 10: P(old) = 80; P(new) = 118; increase = 38 on 80 = 47.5%, confirming the ratio result.

Why Other Options Are Wrong:
20%, 25%, and 27% underestimate the effect because both sides scale appreciably; the exact linear computation gives 47.5%.

Common Pitfalls:
Confusing perimeter (linear) with area (quadratic) scaling, or adding 30% and 100% naively to get 130% which is unrelated to perimeter percent change.

Final Answer:
47.5%