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27 February, 16:58

By the Triangle Inequality Theorem which set of side lengths could create a triangle? A) 5, 10, 4 B) 5, 7, 13 C) 7, 9, 3 D) 10, 4, 5

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  1. 27 February, 20:30
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    The correct answer is C.

    Triangle inequality means 2 sides of the triangle added up must be longer than the remaining side. Therefore, to find the correct answer quickly, we can add up the shortest 2 sides and see if they exceed the remaining side.

    For A,

    5 + 4 = 9

    9 < 10

    Therefore, A is incorrect.

    For B,

    5 + 7 = 12

    12 < 13

    Therefore, B is not correct.

    For C,

    7 + 3 = 10

    10 > 9

    C is the correct answer.

    Heres D, to make sure the answer C is correct.

    4 + 5 = 9

    9 < 10

    D is not correct.

    Let's add up the remaining sides to make sure C completely satisfies the rule.

    9 + 3 = 12

    12 > 7

    7 + 9 = 16

    16 > 3

    Therefore, the answer is C.
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