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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Checkpoint: Rational and irrational numbers

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Q. Which of the following sets of numbers could not represent the three sides of a triangle?

\newline

\{11,13,26\}

\newline

\{13,19,30\}

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\{6,10,15\}

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\{13,19,29\}

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. $\newline$ Calculate if 11 + 13 > 26. $\newline$ $11 + 13 = 24$ , 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. $\newline$ Calculate if 13 + 19 > 30. $\newline$ $13 + 19 = 32$ , 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. $\newline$ Calculate if 13 + 30 > 19 and 19 + 30 > 13. $\newline$ $13 + 30 = 43$ , which is greater than $19$ . $\newline$ $19 + 30 = 49$ , 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. $\newline$ Calculate if 6 + 10 > 15. $\newline$ $6 + 10 = 16$ , 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. $\newline$ Calculate if 6 + 15 > 10 and 10 + 15 > 6. $\newline$ $6 + 15 = 21$ , which is greater than $10$ . $\newline$ $10 + 15 = 25$ , 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.
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. $\newline$ Calculate if 13 + 19 > 29. $\newline$ $13 + 19 = 32$ , which is greater than $29$ .
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. $\newline$ Calculate if 13 + 19 > 29. $\newline$ $13 + 19 = 32$ , which is greater than $29$ .Check the other combinations for the fourth set to ensure all conditions of the Triangle Inequality Theorem are met. $\newline$ Calculate if 13 + 29 > 19 and 19 + 29 > 13. $\newline$ $13 + 29 = 42$ , which is greater than $19$ . $\newline$ $19 + 29 = 48$ , which is greater than $\{13, 19, 29\}$ $0$ .
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. $\newline$ Calculate if 13 + 19 > 29. $\newline$ $13 + 19 = 32$ , which is greater than $29$ .Check the other combinations for the fourth set to ensure all conditions of the Triangle Inequality Theorem are met. $\newline$ Calculate if 13 + 29 > 19 and 19 + 29 > 13. $\newline$ $13 + 29 = 42$ , which is greater than $19$ . $\newline$ $19 + 29 = 48$ , which is greater than $\{13, 19, 29\}$ $0$ .Since all conditions are met for the fourth set, $\{13, 19, 29\}$ could represent the sides of a triangle.