Which of the following sets of numbers could represent the three sides of a triangle? {12,20,34} {13,25,38} {6,13,19} {15,24,36}

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Which of the following sets of numbers could represent the three sides of a triangle?  {12,20,34}  {13,25,38}  {6,13,19}  {15,24,36}

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Understand Triangle Inequality Theorem: Identify the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.Test First Set of Numbers: Test the first set of numbers {12, 20, 34} to see if they satisfy the Triangle Inequality Theorem. Check if 12 + 20 > 34, 12 + 34 > 20, and 20 + 34 > 12. 12 + 20 = 32, which is not greater than 34.First Set Does Not Satisfy Theorem: Since 12 + 20 is not greater than 34, the first set of numbers {12, 20, 34} does not satisfy the Triangle Inequality Theorem and cannot represent the sides of a triangle.Test Second Set of Numbers: Test the second set of numbers {13, 25, 38} to see if they satisfy the Triangle Inequality Theorem. Check if 13 + 25 > 38, 13 + 38 > 25, and 25 + 38 > 13. 13 + 25 = 38, which is not greater than 38.Second Set Does Not Satisfy Theorem: Since 13 + 25 is not greater than 38, the second set of numbers {13, 25, 38} does not satisfy the Triangle Inequality Theorem and cannot represent the sides of a triangle.Test Third Set of Numbers: Test the third set of numbers {6, 13, 19} to see if they satisfy the Triangle Inequality Theorem. Check if 6 + 13 > 19, 6 + 19 > 13, and 13 + 19 > 6. 6 + 13 = 19, which is not greater than 19.Third Set Does Not Satisfy Theorem: Since 6 + 13 is not greater than 19, the third set of numbers {6, 13, 19} does not satisfy the Triangle Inequality Theorem and cannot represent the sides of a triangle.Test Fourth Set of Numbers: Test the fourth set of numbers {15, 24, 36} to see if they satisfy the Triangle Inequality Theorem. Check if 15 + 24 > 36, 15 + 36 > 24, and 24 + 36 > 15. 15 + 24 = 39, which is greater than 36. 15 + 36 = 51, which is greater than 24. 24 + 36 = 60, which is greater than 15.Fourth Set Satisfies Theorem: Since all the inequalities are satisfied for the fourth set of numbers {15, 24, 36}, this set does satisfy the Triangle Inequality Theorem and can represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{12,20,34\}$ $\newline$ $\{13,25,38\}$ $\newline$ $\{6,13,19\}$ $\newline$ $\{15,24,36\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{12,20,34} \{12,20,34\} {12,20,34}\newline{13,25,38} \{13,25,38\} {13,25,38}\newline{6,13,19} \{6,13,19\} {6,13,19}\newline{15,24,36} \{15,24,36\} {15,24,36}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{12,20,34\}$ $\newline$ $\{13,25,38\}$ $\newline$ $\{6,13,19\}$ $\newline$ $\{15,24,36\}$