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The perimeter of a triangle is 53 in. The shortest side is 10 in. less than the longest side. The middle side is 19 in. less than the combined lengths of the
shortest and longest sides. Find the lengths of the three sides.

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sqdancefan

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Answer:

  • shortest: 13 in
  • middle: 17 in
  • longest: 23 in

Step-by-step explanation:

Let s represent the shortest side. Then the longest side is (s+10) and the middle side is (s+(s+10)-19). The perimeter is the sum of the sides.

  s + (2s-9) +(s+10) = 53

  4s +1 = 53

  s = (53 -1)/4 = 13

The side lengths are ...

  • shortest: 13 in
  • middle: 17 in
  • longest: 23 in

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