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Geometry

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In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?

  • Geometry - ,

    One side = L units.
    2nd side = 3L units.
    3rd side = 15 units.

    3L < 15
    L < 5
    L = 4 = Largest possible integer.
    3L = 3*4 = 12.

    P = 4 + 12 + 15 = 31 = Max. possible
    perimeter.

  • Geometry - ,

    for sides a<b<c
    c-b < a < c+b

    So, if 3L is the longest side

    15-L < 3L < L+15
    15 < 4L < 2L+15
    L > 3.75
    L < 7.5

    So, the extreme is 7,15,21 for a perimeter of 43

  • Geometry - ,

    thank you

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