Which of the following sets of numbers could represent the three sides of a triangle? {8,18,24} {14,29,45} {8,23,31} {10,16,28}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {8,18,24}  {14,29,45}  {8,23,31}  {10,16,28}

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 {8,18,24}: Apply the Triangle Inequality Theorem to the first set {8,18,24}. Check if 8 + 18 > 24, 8 + 24 > 18, and 18 + 24 > 8. Calculation: 8 + 18 = 26, 8 + 24 = 32, 18 + 24 = 42. Since 26 > 24, 32 > 18, and 42 > 8, all conditions are satisfied.Apply Theorem to Set {14,29,45}: Apply the Triangle Inequality Theorem to the second set {14,29,45}. Check if 14 + 29 > 45, 14 + 45 > 29, and 29 + 45 > 14. Calculation: 14 + 29 = 43, 14 + 45 = 59, 29 + 45 = 74. Since 43 is not greater than 45, this set does not satisfy the Triangle Inequality Theorem.Apply Theorem to Set {8,23,31}: Apply the Triangle Inequality Theorem to the third set {8,23,31}. Check if 8 + 23 > 31, 8 + 31 > 23, and 23 + 31 > 8. Calculation: 8 + 23 = 31, 8 + 31 = 39, 23 + 31 = 54. Since 31 is not greater than 31, this set does not satisfy the Triangle Inequality Theorem.Apply Theorem to Set {10,16,28}: Apply the Triangle Inequality Theorem to the fourth set {10,16,28}. Check if 10 + 16 > 28, 10 + 28 > 16, and 16 + 28 > 10. Calculation: 10 + 16 = 26, 10 + 28 = 38, 16 + 28 = 44. Since 26 is not greater than 28, this set does not satisfy the Triangle Inequality Theorem.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{8,18,24\}$ $\newline$ $\{14,29,45\}$ $\newline$ $\{8,23,31\}$ $\newline$ $\{10,16,28\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{8,18,24} \{8,18,24\} {8,18,24}\newline{14,29,45} \{14,29,45\} {14,29,45}\newline{8,23,31} \{8,23,31\} {8,23,31}\newline{10,16,28} \{10,16,28\} {10,16,28}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{8,18,24\}$ $\newline$ $\{14,29,45\}$ $\newline$ $\{8,23,31\}$ $\newline$ $\{10,16,28\}$