Which of the following sets of numbers could not represent the three sides of a triangle? {11,13,26} {13,19,30} {6,10,15} {13,19,29}

Question

Which of the following sets of numbers could not represent the three sides of a triangle?  {11,13,26}  {13,19,30}  {6,10,15}  {13,19,29}

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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 {11, 13, 26} to see if they satisfy the Triangle Inequality Theorem. Calculate if 11 + 13 > 26. 11 + 13 = 24, which is not greater than 26.First Set Not Satisfactory: Since 24 is not greater than 26, the set {11, 13, 26} does not satisfy the Triangle Inequality Theorem and therefore cannot represent the sides of a triangle.Check Second Set: Check the second set of numbers {13, 19, 30} to see if they satisfy the Triangle Inequality Theorem. Calculate if 13 + 19 > 30. 13 + 19 = 32, which is greater than 30.Second Set Satisfactory: Check the other combinations for the second set to ensure all conditions of the Triangle Inequality Theorem are met. Calculate if 13 + 30 > 19 and 19 + 30 > 13. 13 + 30 = 43, which is greater than 19. 19 + 30 = 49, which is greater than 13.Check Third Set: Since all conditions are met for the second set, {13, 19, 30} could represent the sides of a triangle.Third Set Satisfactory: Check the third set of numbers {6, 10, 15} to see if they satisfy the Triangle Inequality Theorem. Calculate if 6 + 10 > 15. 6 + 10 = 16, which is greater than 15.Check Fourth Set: Check the other combinations for the third set to ensure all conditions of the Triangle Inequality Theorem are met. Calculate if 6 + 15 > 10 and 10 + 15 > 6. 6 + 15 = 21, which is greater than 10. 10 + 15 = 25, which is greater than 6.Fourth Set Satisfactory: Since all conditions are met for the third set, {6, 10, 15} could represent the sides of a triangle.Check the fourth set of numbers {13, 19, 29} to see if they satisfy the Triangle Inequality Theorem. Calculate if 13 + 19 > 29. 13 + 19 = 32, which is greater than 29.Check the other combinations for the fourth set to ensure all conditions of the Triangle Inequality Theorem are met. Calculate if 13 + 29 > 19 and 19 + 29 > 13. 13 + 29 = 42, which is greater than 19. 19 + 29 = 48, which is greater than 13.Since all conditions are met for the fourth set, {13, 19, 29} could represent the sides of a triangle.

Which of the following sets of numbers could not represent the three sides of a triangle? $\newline$ $\{11,13,26\}$ $\newline$ $\{13,19,30\}$ $\newline$ $\{6,10,15\}$ $\newline$ $\{13,19,29\}$

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Which of the following sets of numbers could not represent the three sides of a triangle?\newline{11,13,26} \{11,13,26\} {11,13,26}\newline{13,19,30} \{13,19,30\} {13,19,30}\newline{6,10,15} \{6,10,15\} {6,10,15}\newline{13,19,29} \{13,19,29\} {13,19,29}

Which of the following sets of numbers could not represent the three sides of a triangle? $\newline$ $\{11,13,26\}$ $\newline$ $\{13,19,30\}$ $\newline$ $\{6,10,15\}$ $\newline$ $\{13,19,29\}$