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Given three side lengths, how many triangles can be formed?

Posted on October 22, 2021 By Ceasar6071 5 Comments on Given three side lengths, how many triangles can be formed?

Given three side lengths, how many triangles can be formed?

Mathematics

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Comments (5) on “Given three side lengths, how many triangles can be formed?”

  1. rue61 says:
    October 23, 2021 at 11:22 am

    Given three side lengths, for example, a, b and c, you can form the triangle when

    [tex]a+bc,\\ a+cb,\\ b+ca.[/tex]

    If this property holds, then one triangle you can form. Each next triangle with the same sides lengths will be congruent to the first triangle by SSS postulate.

    SSS postulate says: If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

    1 triangle, correct option is A.

    Reply
  2. chameleonsarelife says:
    October 23, 2021 at 2:39 pm

    We know that

    In a triangle, the combined lengths of any two sides must always be greater than the length of the third side. (Triangle Inequality Theorem)

    If all three side lengths are given and the combined length of two sides is greater than the length of the third side.

    then 

     one unique triangle can be made

    Reply
  3. jeovontamarley says:
    October 23, 2021 at 9:45 pm

    I believe the correct answer from the choices listed above is option 1. Given three side lengths, there would be 1 triangle that can be formed. For a given set of side length only one orientation of these lines that can be made.

    Hope this answers the question. Have a nice day.

    Reply
  4. juliemiddleton05 says:
    October 24, 2021 at 1:55 am

    Given three side lengths, there would be 1 triangle that can be formed.

    Reply
  5. jsavagejsavage8596 says:
    October 24, 2021 at 4:16 am

    The answer would be 3 or 4 triangles.

    Reply

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