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Math Help - Triangular Inequality

  1. #1
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    Question Triangular Inequality

    Can someone please help me with this problem?

    The length of two sides of a triangle are 4 cm & 6 cm. Between what two measures should the length of the third side fall?

    Thanks,

    Ron
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  2. #2
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    Quote Originally Posted by rn5a View Post
    Can someone please help me with this problem?

    The length of two sides of a triangle are 4 cm & 6 cm. Between what two measures should the length of the third side fall?

    Thanks,

    Ron
    Try to think how to construct a triangle where the third side is 2 cm. You won't be able to because it won't reach. (You can think of drawing the 6 cm side on paper, and then placing the point of a compass at one endpoint, and tracing a circle of radius 4 cm. Then do the same on the other end with 2 cm. You can see they won't intersect to form a triangle, only a "degenerate triangle" which is a line segment.)

    Similarly, you won't be able to construct a triangle when the third side length is 10.

    So it's 2 < x < 10.
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  3. #3
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    Thanks mate for your response but what I would like to know is how did you come to the conclusion 2 < x < 10. Is there any formula for it or did you first try 2, then 3, then 4 so & so forth till 10 (or may be more). Did you do it by the trial & error method?

    Thanks once again,

    Ron
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  4. #4
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    Quote Originally Posted by rn5a View Post
    Thanks mate for your response but what I would like to know is how did you come to the conclusion 2 < x < 10. Is there any formula for it or did you first try 2, then 3, then 4 so & so forth till 10 (or may be more). Did you do it by the trial & error method?

    Thanks once again,

    Ron
    Quoting Wikipedia, "In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side." (source)

    I did not try random numbers. My explanation in parentheses was to explain how I got there, because this is an intuitive inequality. The numbers are obtained as follows: 6-4 = 2. 6+4 = 10.
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