If two sides of a triangle are of measures 15 and 28, what is the range of possible values for the third side x?

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If two sides of a triangle are of measures 15 and 28, what is the range of possible values for the third side x?

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    2021-11-25T21:53:04+00:00


    Let side a = 5. Let side b = 9. Then the triangle has
    sides

    a=5, b=9, and c=?. Any side of a triangle must be less
    than the other two sides added together, so

    a < b+c, b < a+c, and c < a+b

    Substituting:

    5 < 9+c, 9 < 5+c, and c < 5+9

    Solving all three for c:

    -4 < c, 4 < c, c < 14

    The first one is of course true, so ignore it.
    Put the second and third together and get

    4 < c < 14

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