Which of the following sets of numbers could represent the three sides of a triangle? {13,27,41} {8,21,29} {14,18,34} {4,16,17}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {13,27,41}  {8,21,29}  {14,18,34}  {4,16,17}

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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.Check First Set: Check the first set of numbers {13, 27, 41} to see if they satisfy the Triangle Inequality Theorem. We need to check if: 13 + 27 > 41, 13 + 41 > 27, and 27 + 41 > 13.Perform First Set Calculations: Perform the calculations for the first set. 13 + 27 = 40, which is not greater than 41. This means that the first set of numbers cannot represent the sides of a triangle.Check Second Set: Check the second set of numbers {8, 21, 29} to see if they satisfy the Triangle Inequality Theorem. We need to check if: 8 + 21 > 29, 8 + 29 > 21, and 21 + 29 > 8.Perform Second Set Calculations: Perform the calculations for the second set. 8 + 21 = 29, which is not greater than 29. This means that the second set of numbers cannot represent the sides of a triangle.Check Third Set: Check the third set of numbers {14, 18, 34} to see if they satisfy the Triangle Inequality Theorem. We need to check if: 14 + 18 > 34, 14 + 34 > 18, and 18 + 34 > 14.Perform Third Set Calculations: Perform the calculations for the third set. 14 + 18 = 32, which is not greater than 34. This means that the third set of numbers cannot represent the sides of a triangle.Check Fourth Set: Check the fourth set of numbers {4, 16, 17} to see if they satisfy the Triangle Inequality Theorem. We need to check if: 4 + 16 > 17, 4 + 17 > 16, and 16 + 17 > 4.Perform Fourth Set Calculations: Perform the calculations for the fourth set. 4 + 16 = 20, which is greater than 17. 4 + 17 = 21, which is greater than 16. 16 + 17 = 33, which is greater than 4. All conditions are satisfied, so the fourth set of numbers can represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{13,27,41\}$ $\newline$ $\{8,21,29\}$ $\newline$ $\{14,18,34\}$ $\newline$ $\{4,16,17\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{13,27,41} \{13,27,41\} {13,27,41}\newline{8,21,29} \{8,21,29\} {8,21,29}\newline{14,18,34} \{14,18,34\} {14,18,34}\newline{4,16,17} \{4,16,17\} {4,16,17}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{13,27,41\}$ $\newline$ $\{8,21,29\}$ $\newline$ $\{14,18,34\}$ $\newline$ $\{4,16,17\}$