Square – side increased by 25%: If each side of a square is increased by 25% (one–fourth more than the original), by what percentage does its area change overall?
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A56.25%
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B36.25%
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C16.25%
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D12.25%
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ENone of these
Answer
Correct Answer: 56.25%
Explanation
Introduction / Context:Questions that ask for the percentage change in area when each side changes are classic geometry percentage problems. Area of a square depends on the square of its side length, so proportional side changes scale area quadratically.
Given Data / Assumptions:
- Original square side = s.
- New side = s increased by 25% = 1.25*s.
- We need overall % change in area.
Concept / Approach:The area of a square is side^2. If side is multiplied by k, area is multiplied by k^2. Percentage change = (new/old − 1) * 100%.
Step-by-Step Solution:
Original area = s^2.New side = 1.25*s.New area = (1.25*s)^2 = 1.5625*s^2.Factor increase = 1.5625.Percentage change = (1.5625 − 1)*100% = 0.5625*100% = 56.25%.Verification / Alternative check:1.25 = 5/4; (5/4)^2 = 25/16 = 1.5625 → increase 9/16 = 0.5625 → 56.25%.
Why Other Options Are Wrong:
- 36.25%, 16.25%, 12.25% underestimate the quadratic effect; they may stem from linear thinking.
- None of these is invalid because 56.25% is available.
Common Pitfalls:Using 25% directly on area (linear) instead of squaring the side-scale factor; forgetting that area scales with side^2.
Final Answer:56.25%