A rectangle's length increases by 60%. By what percentage must the width decrease to preserve the area?
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Answer: A. 37 ½ %
Explanation
Preserving a constant rectangular area requires adjusting the second dimension inversely to the first dimension change. Increasing length by sixty percent creates a new length multiplier equal to one point six times original. Dividing original width by one point six yields a five-eighths factor reflecting a thirty-seven point five percent cut. Area preservation demands that the product of length and breadth remains identically equal to initial measurements. Mathematical inverse proportions ensure that scaling one variable up requires scaling the other variable down proportionally. Fractions like three-eighths convert cleanly into decimal percentages equal to thirty-seven and a half percent.
Option B recommends sixty percent reduction which incorrectly assumes linear symmetry between percentage increases and decreases. Option C recommends seventy-five percent reduction which overcorrects the dimensional change and shrinks total area. Option D is incorrect because the mathematically precise answer thirty-seven point five percent is listed in option A.
- Subject
- Mathematics
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- Mathematics
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- —
- Difficulty
- medium
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