Maintain area with a 25% longer length:\nIf the length of a rectangle is increased by 25%, by what percentage must the breadth decrease so that the area remains unchanged?

Introduction / Context:
Area of a rectangle is length * breadth. If one dimension is scaled, the other must scale reciprocally to preserve the product. A 25% increase corresponds to a scale factor of 1.25; the breadth must be multiplied by 1/1.25 to keep area constant.

Given Data / Assumptions:
Initial area A = L * B. New length L′ = 1.25L. Required B′ such that L′ * B′ = A.

Concept / Approach:
Set L′ * B′ = L * B ⇒ (1.25L)*B′ = L*B ⇒ B′ = B/1.25. Convert B′ = 0.8B into a percentage decrease from B: decrease = (1 − 0.8)*100% = 20% decrease.

Step-by-Step Solution:

Verification / Alternative check:
Example: L = 100, B = 100 ⇒ A = 10000. New L′ = 125; B′ = 80; area 125*80 = 10000 (unchanged).

Why Other Options Are Wrong:
25%, 30%, 40% do not correspond to the exact reciprocal adjustment of 1.25.

Common Pitfalls:
Subtracting 25% directly from breadth; area constraints demand multiplicative reciprocity, not additive subtraction.

Final Answer:
20%