Which of the following sets of numbers could represent the three sides of a triangle? {4,10,14} {12,25,36} {6,8,14} {15,30,46}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {4,10,14}  {12,25,36}  {6,8,14}  {15,30,46}

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 {4,10,14}: Apply the Triangle Inequality Theorem to the first set {4,10,14}. Check if 4 + 10 > 14, 4 + 14 > 10, and 10 + 14 > 4. 4 + 10 = 14 which is not greater than 14, so the first set does not satisfy the Triangle Inequality Theorem.Apply Theorem to Set {12,25,36}: Apply the Triangle Inequality Theorem to the second set {12,25,36}. Check if 12 + 25 > 36, 12 + 36 > 25, and 25 + 36 > 12. 12 + 25 = 37 which is greater than 36, 12 + 36 = 48 which is greater than 25, but 25 + 36 = 61 which is not greater than 12, so the second set does not satisfy the Triangle Inequality Theorem.Apply Theorem to Set {6,8,14}: Apply the Triangle Inequality Theorem to the third set {6,8,14}. Check if 6 + 8 > 14, 6 + 14 > 8, and 8 + 14 > 6. 6 + 8 = 14 which is not greater than 14, so the third set does not satisfy the Triangle Inequality Theorem.Apply Theorem to Set {15,30,46}: Apply the Triangle Inequality Theorem to the fourth set {15,30,46}. Check if 15 + 30 > 46, 15 + 46 > 30, and 30 + 46 > 15. 15 + 30 = 45 which is not greater than 46, so 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? $\newline$ $\{4,10,14\}$ $\newline$ $\{12,25,36\}$ $\newline$ $\{6,8,14\}$ $\newline$ $\{15,30,46\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{4,10,14} \{4,10,14\} {4,10,14}\newline{12,25,36} \{12,25,36\} {12,25,36}\newline{6,8,14} \{6,8,14\} {6,8,14}\newline{15,30,46} \{15,30,46\} {15,30,46}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{4,10,14\}$ $\newline$ $\{12,25,36\}$ $\newline$ $\{6,8,14\}$ $\newline$ $\{15,30,46\}$