Which of the following sets of numbers could represent the three sides of a triangle? {12,23,32} {13,17,30} {14,27,41} {12,21,35}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {12,23,32}  {13,17,30}  {14,27,41}  {12,21,35}

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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, 23, 32} to see if they satisfy the Triangle Inequality Theorem. Check if 12 + 23 > 32, 12 + 32 > 23, and 23 + 32 > 12. Perform the calculations: 12 + 23 = 35, 12 + 32 = 44, 23 + 32 = 55. All three conditions are true: 35 > 32, 44 > 23, and 55 > 12.Test Second Set of Numbers: Test the second set of numbers {13, 17, 30} to see if they satisfy the Triangle Inequality Theorem. Check if 13 + 17 > 30, 13 + 30 > 17, and 17 + 30 > 13. Perform the calculations: 13 + 17 = 30, 13 + 30 = 43, 17 + 30 = 47. The first condition is not true: 13 + 17 = 30 is not greater than 30. This set of numbers cannot represent the sides of a triangle.Test Third Set of Numbers: Test the third set of numbers {14, 27, 41} to see if they satisfy the Triangle Inequality Theorem. Check if 14 + 27 > 41, 14 + 41 > 27, and 27 + 41 > 14. Perform the calculations: 14 + 27 = 41, 14 + 41 = 55, 27 + 41 = 68. The first condition is not true: 14 + 27 = 41 is not greater than 41. This set of numbers cannot represent the sides of a triangle.Test Fourth Set of Numbers: Test the fourth set of numbers {12, 21, 35} to see if they satisfy the Triangle Inequality Theorem. Check if 12 + 21 > 35, 12 + 35 > 21, and 21 + 35 > 12. Perform the calculations: 12 + 21 = 33, 12 + 35 = 47, 21 + 35 = 56. The first condition is not true: 12 + 21 = 33 is not greater than 35. This set of numbers cannot represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{12,23,32\}$ $\newline$ $\{13,17,30\}$ $\newline$ $\{14,27,41\}$ $\newline$ $\{12,21,35\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{12,23,32} \{12,23,32\} {12,23,32}\newline{13,17,30} \{13,17,30\} {13,17,30}\newline{14,27,41} \{14,27,41\} {14,27,41}\newline{12,21,35} \{12,21,35\} {12,21,35}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{12,23,32\}$ $\newline$ $\{13,17,30\}$ $\newline$ $\{14,27,41\}$ $\newline$ $\{12,21,35\}$