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A rectangular community garden plot has a length that is 4 meters longer than its width. If the area of the plot is 96 square meters, what is the width of the plot, in meters?
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Correct answer
B
Translate the two clauses into algebra. Let the width be w. The length is 4 meters longer, so the length is w + 4. The area is length × width, so (w + 4) × w = 96. Expanding gives w² + 4w = 96, or w² + 4w − 96 = 0. Factor by finding two numbers whose product is −96 and whose sum is 4, which are 12 and −8, so (w + 12)(w − 8) = 0. The roots are w = −12 and w = 8. A width cannot be negative, so discard w = −12 and keep w = 8. The width is 8 meters, and the length is 12 meters, which checks: 8 × 12 = 96. The answer is (B).
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