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19 August, 05:05

Two sides of a triangle have the measures 7 and 10. Is it true or false that the range of possible measures for the third side is 7

True

False

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Answers (1)
  1. 19 August, 07:18
    0
    True

    Step-by-step explanation:

    We know that The triangle inequality states that the sum of the two sides of the triangle is always greater than the third side.

    Here given that two sides of the triangle are 7 and 10

    Let the third side be x

    Here a = 7, b = 10, c = x

    According to the triangle inequality

    a + b > c

    7 + 10 > x

    x < 17

    Also c + b > a

    x + 10 > 7

    x > - 3

    Also a + c > b

    7 + x > 10

    x > 3

    Combining all the above results we get

    3 < x < 17

    All the values of x in the above region forms a triangle

    Given x values lies in the region so they form a triangle
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