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Assume that the sides of triangles are limited to
whole-number measures. How many different
triangles have a perimeter of 12 meters? Explain
how you determined this.

  • math -

    The constraints are as follows:
    any two sides of a triangle must be longer than the third side, so 1,6,5 because 1+5=6 (not greater) would not work, nor 2,2,8, because 2+2<8, etc.
    So make a table of sides, and cross out the ones that do not work.

    The sides a, b and c must be in ascending order so that you do not repeat the same triangles.

    So the method of solution is by tabulation.

    a b c OK?
    1 4 7 X
    1 5 6 X
    2 4 6 X
    2 5 5 OK
    3 3 6 X
    3 4 5 OK
    4 4 4 OK

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