which set of numbers could be the lengths of the sides of a triangle
A.{6,7,13}
B.{3,6,9}
C.{5,5,11}
D.{12,13,20}

According to the triangle inequality theorem, any two sides' sums in a triangle must be bigger than the length of the third side. If a, b, and c are the lengths of a triangle's sides, then the sum of a and b's lengths is greater than c's length. Similar to how a+ c > b, b + c > a. It is not possible to create a triangle using the specified side lengths in any instance where they are unable to satisfy these requirements.

In the question, we are asked for the set of numbers from the options that could be the lengths of the sides of a triangle.

A. {6, 7, 13}. Since 6 + 7 is not greater than the third side 13, the given lengths cannot make a triangle.
B. {3, 6, 9}. Since 3 + 6 is not greater than the third side 9, the given lengths cannot make a triangle.
C. {5, 5, 11}. Since 5 + 5 is not greater than the third side 11, the given lengths cannot make a triangle.
D. {12, 13, 20}. Since 12 + 13 > 20, 13 + 20 > 12, and 12 + 20 > 13, the triangle inequality theorem is satisfied and thus, the given sides can make a triangle.

Thus, the lengths of the sides of a triangle can be the set of numbers {12, 13, 20}, making option D the right choice.

Learn more about the triangle inequality theorem at

https://brainly.com/question/309896

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which set of numbers could be the lengths of the sides of a triangle A.{6,7,13} B.{3,6,9} C.{5,5,11} D.{12,13,20}

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which set of numbers could be the lengths of the sides of a triangle
A.{6,7,13}
B.{3,6,9}
C.{5,5,11}
D.{12,13,20}