Which of the following sets of numbers could represent the three sides of a triangle? {4,10,12} {4,17,21} {4,14,20} {13,18,31}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {4,10,12}  {4,17,21}  {4,14,20}  {13,18,31}

Bytelearn · Accepted Answer

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 {4,10,12}: Apply the Triangle Inequality Theorem to the first set {4,10,12}. Check if 4 + 10 > 12, 4 + 12 > 10, and 10 + 12 > 4. Calculations: 4 + 10 = 14, 4 + 12 = 16, 10 + 12 = 22. Since 14 > 12, 16 > 10, and 22 > 4, all conditions are satisfied.Apply Theorem to Set {4,17,21}: Apply the Triangle Inequality Theorem to the second set {4,17,21}. Check if 4 + 17 > 21, 4 + 21 > 17, and 17 + 21 > 4. Calculations: 4 + 17 = 21, 4 + 21 = 25, 17 + 21 = 38. Since 21 is not greater than 21, the condition 4 + 17 > 21 is not satisfied.Apply Theorem to Set {4,14,20}: Apply the Triangle Inequality Theorem to the third set {4,14,20}. Check if 4 + 14 > 20, 4 + 20 > 14, and 14 + 20 > 4. Calculations: 4 + 14 = 18, 4 + 20 = 24, 14 + 20 = 34. Since 18 is not greater than 20, the condition 4 + 14 > 20 is not satisfied.Apply Theorem to Set {13,18,31}: Apply the Triangle Inequality Theorem to the fourth set {13,18,31}. Check if 13 + 18 > 31, 13 + 31 > 18, and 18 + 31 > 13. Calculations: 13 + 18 = 31, 13 + 31 = 44, 18 + 31 = 49. Since 31 is not greater than 31, the condition 13 + 18 > 31 is not satisfied.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{4,10,12\}$ $\newline$ $\{4,17,21\}$ $\newline$ $\{4,14,20\}$ $\newline$ $\{13,18,31\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{4,10,12} \{4,10,12\} {4,10,12}\newline{4,17,21} \{4,17,21\} {4,17,21}\newline{4,14,20} \{4,14,20\} {4,14,20}\newline{13,18,31} \{13,18,31\} {13,18,31}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{4,10,12\}$ $\newline$ $\{4,17,21\}$ $\newline$ $\{4,14,20\}$ $\newline$ $\{13,18,31\}$