Which of the following sets of numbers could represent the three sides of a triangle? {4,14,18} {7,11,19} {4,8,10} {10,24,35}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {4,14,18}  {7,11,19}  {4,8,10}  {10,24,35}

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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 Set 1: Apply the Triangle Inequality Theorem to the first set of numbers {4,14,18}. Check if 4 + 14 > 18, 4 + 18 > 14, and 14 + 18 > 4. Calculations: 4 + 14 = 18, 4 + 18 = 22, 14 + 18 = 32. Since 4 + 14 is not greater than 18, the first set does not satisfy the Triangle Inequality Theorem.Apply Theorem to Set 2: Apply the Triangle Inequality Theorem to the second set of numbers {7,11,19}. Check if 7 + 11 > 19, 7 + 19 > 11, and 11 + 19 > 7. Calculations: 7 + 11 = 18, 7 + 19 = 26, 11 + 19 = 30. Since 7 + 11 is not greater than 19, the second set does not satisfy the Triangle Inequality Theorem.Apply Theorem to Set 3: Apply the Triangle Inequality Theorem to the third set of numbers {4,8,10}. Check if 4 + 8 > 10, 4 + 10 > 8, and 8 + 10 > 4. Calculations: 4 + 8 = 12, 4 + 10 = 14, 8 + 10 = 18. All sums are greater than the third side, so the third set satisfies the Triangle Inequality Theorem.Apply Theorem to Set 4: Apply the Triangle Inequality Theorem to the fourth set of numbers {10,24,35}. Check if 10 + 24 > 35, 10 + 35 > 24, and 24 + 35 > 10. Calculations: 10 + 24 = 34, 10 + 35 = 45, 24 + 35 = 59. Since 10 + 24 is not greater than 35, the fourth set does not satisfy the Triangle Inequality Theorem.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{4,14,18\}$ $\newline$ $\{7,11,19\}$ $\newline$ $\{4,8,10\}$ $\newline$ $\{10,24,35\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{4,14,18} \{4,14,18\} {4,14,18}\newline{7,11,19} \{7,11,19\} {7,11,19}\newline{4,8,10} \{4,8,10\} {4,8,10}\newline{10,24,35} \{10,24,35\} {10,24,35}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{4,14,18\}$ $\newline$ $\{7,11,19\}$ $\newline$ $\{4,8,10\}$ $\newline$ $\{10,24,35\}$