Which of the following sets of numbers could represent the three sides of a triangle? {5,17,23} {6,20,25} {5,17,24} {10,13,25}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {5,17,23}  {6,20,25}  {5,17,24}  {10,13,25}

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Recall Triangle Inequality Theorem: Recall 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. Apply Theorem to First Set: Apply the Triangle Inequality Theorem to the first set {5,17,23}. Check if 5 + 17 > 23, 5 + 23 > 17, and 17 + 23 > 5. Check First Set Calculations: Perform the calculations for the first set: 5 + 17 = 22, which is not greater than 23. Therefore, the first set {5,17,23} cannot represent the sides of a triangle. Apply Theorem to Second Set: Apply the Triangle Inequality Theorem to the second set {6,20,25}. Check if 6 + 20 > 25, 6 + 25 > 20, and 20 + 25 > 6. Check Second Set Calculations: Perform the calculations for the second set: 6 + 20 = 26, which is greater than 25. Now check the other two conditions. Apply Theorem to Third Set: For the second set, check if 6 + 25 > 20, which is 31 > 20, and 20 + 25 > 6, which is 45 > 6. All conditions are satisfied, so the second set {6,20,25} could represent the sides of a triangle. Check Third Set Calculations: Apply the Triangle Inequality Theorem to the third set {5,17,24}. Check if 5 + 17 > 24, 5 + 24 > 17, and 17 + 24 > 5. Apply Theorem to Fourth Set: Perform the calculations for the third set: 5 + 17 = 22, which is not greater than 24. Therefore, the third set {5,17,24} cannot represent the sides of a triangle. Check Fourth Set Calculations: Apply the Triangle Inequality Theorem to the fourth set {10,13,25}. Check if 10 + 13 > 25, 10 + 25 > 13, and 13 + 25 > 10. Perform the calculations for the fourth set: 10 + 13 = 23, which is not greater than 25. Therefore, the fourth set {10,13,25} cannot represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{5,17,23\}$ $\newline$ $\{6,20,25\}$ $\newline$ $\{5,17,24\}$ $\newline$ $\{10,13,25\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{5,17,23} \{5,17,23\} {5,17,23}\newline{6,20,25} \{6,20,25\} {6,20,25}\newline{5,17,24} \{5,17,24\} {5,17,24}\newline{10,13,25} \{10,13,25\} {10,13,25}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{5,17,23\}$ $\newline$ $\{6,20,25\}$ $\newline$ $\{5,17,24\}$ $\newline$ $\{10,13,25\}$