Which of the following sets of numbers could not represent the three sides of a triangle? {6,20,24} {6,9,13} {10,25,36} {11,23,33}

Question

Which of the following sets of numbers could not represent the three sides of a triangle?  {6,20,24}  {6,9,13}  {10,25,36}  {11,23,33}

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Triangle Inequality Theorem: To determine if a set of numbers can represent the sides of a triangle, we use the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. We will apply this theorem to each set of numbers.Set {6,20,24}: First, we check the set {6,20,24}. According to the triangle inequality theorem, we should have 6 + 20 > 24, 6 + 24 > 20, and 20 + 24 > 6. Let's check these inequalities: 6 + 20 = 26, which is greater than 24. 6 + 24 = 30, which is greater than 20. 20 + 24 = 44, which is greater than 6. All inequalities hold true, so this set could represent the sides of a triangle.Set {6,9,13}: Next, we check the set {6,9,13}. According to the triangle inequality theorem, we should have 6 + 9 > 13, 6 + 13 > 9, and 9 + 13 > 6. Let's check these inequalities: 6 + 9 = 15, which is greater than 13. 6 + 13 = 19, which is greater than 9. 9 + 13 = 22, which is greater than 6. All inequalities hold true, so this set could represent the sides of a triangle.Set {10,25,36}: Now, we check the set {10,25,36}. According to the triangle inequality theorem, we should have 10 + 25 > 36, 10 + 36 > 25, and 25 + 36 > 10. Let's check these inequalities: 10 + 25 = 35, which is not greater than 36. This inequality does not hold true. Therefore, this set cannot represent the sides of a triangle.Set {11,23,33}: Finally, we check the set {11,23,33}. According to the triangle inequality theorem, we should have 11 + 23 > 33, 11 + 33 > 23, and 23 + 33 > 11. Let's check these inequalities: 11 + 23 = 34, which is greater than 33. 11 + 33 = 44, which is greater than 23. 23 + 33 = 56, which is greater than 11. All inequalities hold true, so this set could represent the sides of a triangle.

Which of the following sets of numbers could not represent the three sides of a triangle? $\newline$ $\{6,20,24\}$ $\newline$ $\{6,9,13\}$ $\newline$ $\{10,25,36\}$ $\newline$ $\{11,23,33\}$

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Which of the following sets of numbers could not represent the three sides of a triangle?\newline{6,20,24} \{6,20,24\} {6,20,24}\newline{6,9,13} \{6,9,13\} {6,9,13}\newline{10,25,36} \{10,25,36\} {10,25,36}\newline{11,23,33} \{11,23,33\} {11,23,33}

Which of the following sets of numbers could not represent the three sides of a triangle? $\newline$ $\{6,20,24\}$ $\newline$ $\{6,9,13\}$ $\newline$ $\{10,25,36\}$ $\newline$ $\{11,23,33\}$