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12 March, 15:42

A triangle has sides of 5 and 9. What is a possible length of the third side?

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  1. 12 March, 15:47
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    4 < c < 14e. g : {5, 6, 7, 8, 9, 10, 11, 12, 13}

    Step-by-step explanation:

    Let

    a, b, c - lengths of sides of a triangle

    then:

    a + b > c

    a + c > b

    b + c > a.

    We have

    a = 5, b = 9

    then

    c < 5 + 9 → c < 14 (1)

    5 + c > 9 subtract 5 from both sides

    c > 4 (2)

    9 + c > 4 subtract 9 from both sides

    c > - 5 (3)

    From (1), (2) and (3) we have

    c 4 ∧ c > - 5 → 4 < c < 14
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