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The length of a rectangle is increased by 60 %. By what percent would the width have to be decreased to maintain the same area?

Correct answer: A. 37 ½ %

  • A. 37 ½ %
  • B. 60 %
  • C. 75 %
  • D. none of these

Explanation

A 60% increase makes the length 1.6 times its original value. To keep the area constant, the width must become 1/1.6 = 0.625 of its original value, so its decrease is 1 − 0.625 = 0.375 = 37.5%, or 37 1/2%. Students may choose 60% by assuming the width must decrease by the same percentage as the length increases.

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Percentages express a quantity as parts per hundred and support calculations involving increases, decreases, discounts, commissions, taxes, and successive changes. Questions require distinguishing percentage change from percentage points and identifying the original value when a final value and its percentage change are given.

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