A rectangle's length increases by 60%. By what percentage must its width be reduced to keep the area unchanged?
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Answer: A. 37 ½ %
Explanation
Preserving total rectangle area requires multiplying the adjusted width by the reciprocal of the length factor. An increase in length by sixty percent scales the initial linear dimension by a factor of one point six. Multiplying initial width by five eighths yields a fractional decrease representing thirty seven point five percent. Rectangle area remains constant when any increase in one dimension balances out by an inverse dimensional decrease. Percentages represent proportions out of one hundred and fractions simplify decimal multiplier calculations in geometry problems. Sixty percent increase translates directly to multiplying the original base dimension by one point six.
Option B suggests sixty percent which would incorrectly reduce area rather than preserving original dimensions entirely. Option C suggests seventy-five percent which represents an excessive reduction that would significantly shrink total area. Option D suggests one hundred twenty percent which represents a dimensional increase rather than a percentage reduction.
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- Mathematics
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- Mathematics
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