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A landscaping cooperative encloses a rectangular community plot using exactly 70 meters of fencing along its four sides. The enclosed plot has an area of 304 square meters. What is the length, in meters, of the longer side of the plot?
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Correct answer
B
Let the two side lengths be L and W. The perimeter gives 2(L + W) = 70, so L + W = 35. The area gives L × W = 304. The two sides are therefore the roots of the quadratic t² − 35t + 304 = 0.
Factor it by finding two numbers that multiply to 304 and add to 35: those numbers are 16 and 19, since 16 × 19 = 304 and 16 + 19 = 35. So (t − 16)(t − 19) = 0, giving sides of 16 and 19. The longer side is 19, which is the correct answer (B).
Choice A, 16, is the smaller root: you can factor correctly but still pick the shorter side if you do not re-read which side the question asks for. Choice C, 35, comes from halving the perimeter to get L + W and reporting that sum instead of a single side. Choice D, 38, traps you if you search for any factor pair of 304 (here 8 and 38) and report the larger factor without checking that the two sides must also add to 35, so it satisfies the area but not the perimeter. Choice E, 51, comes from forgetting to halve the perimeter, treating L + W as 70, and estimating one side from that inflated total. Only 19 satisfies both the perimeter and the area, so the answer is B.
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