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a musical triangle has a perimeter of 180 mm. the side of middle length is 2 times as long as the shortest side. the longest side is 3 times as long as the middle side. how long is each side

  • math -

    shortest side -- x
    middle side ----2x
    longest side --- 3(2x) = 6x

    x + 2x + 6x = 180
    9x=180
    x=20

    shortest = 20
    middle = 40
    longest = 120

    BTW, no such triangle is possible, even though a mathematical solution exists.

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