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A vacant city lot is being turned into a neighborhood garden. The neighbors want to fence in a triangular section of the lot and plant flowers there. The longest side of the triangular section is 7 feet shorter than twice the shortest side. The third side is 3 feet longer than the shortest side. The perimeter is 64 feet. How long is each​ side?

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Answer:

  17 ft, 27 ft, 20 ft

Step-by-step explanation:

Let s represent the length of the shortest side. The the longest side is (2s-7) and the third side is (s+3). The perimeter is the sum of the side lengths:

  64 = s +(2s -7) +(s +3)

  64 = 4s -4 . . . . . . . . . . . collect terms

  16 = s -1 . . . . . . . . . . divide by 4

  17 = s . . . . . . . . . add 1

  2s -7 = 2·17 -7 = 27 . . . . . the length of the longest side

  s +3 = 17 +3 = 20 . . . . . . . the length of the third side

The side lengths are 17 feet, 27 feet, and 20 feet.

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