Which of the following sets of numbers could represent the three sides of a triangle? {12,19,31} {10,25,37} {10,15,26} {7,21,27}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {12,19,31}  {10,25,37}  {10,15,26}  {7,21,27}

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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 First Set: Apply the Triangle Inequality Theorem to the first set {12, 19, 31}. Check if the sum of the two smallest numbers is greater than the largest number: 12 + 19 > 31? Calculate First Set: Perform the calculation for the first set: 12 + 19 = 31. Since 31 is not greater than 31, the first set does not satisfy the Triangle Inequality Theorem. Apply Theorem to Second Set: Apply the Triangle Inequality Theorem to the second set {10, 25, 37}. Check if the sum of the two smallest numbers is greater than the largest number: 10 + 25 > 37? Calculate Second Set: Perform the calculation for the second set: 10 + 25 = 35. Since 35 is not greater than 37, the second set does not satisfy the Triangle Inequality Theorem. Apply Theorem to Third Set: Apply the Triangle Inequality Theorem to the third set {10, 15, 26}. Check if the sum of the two smallest numbers is greater than the largest number: 10 + 15 > 26? Calculate Third Set: Perform the calculation for the third set: 10 + 15 = 25. Since 25 is not greater than 26, the third set does not satisfy the Triangle Inequality Theorem. Apply Theorem to Fourth Set: Apply the Triangle Inequality Theorem to the fourth set {7, 21, 27}. Check if the sum of the two smallest numbers is greater than the largest number: 7 + 21 > 27? Calculate Fourth Set: Perform the calculation for the fourth set: 7 + 21 = 28. Since 28 is greater than 27, the fourth set satisfies the Triangle Inequality Theorem. Conclude Valid Triangle Set: Conclude that the fourth set {7, 21, 27} is the only set that could represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{12,19,31\}$ $\newline$ $\{10,25,37\}$ $\newline$ $\{10,15,26\}$ $\newline$ $\{7,21,27\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{12,19,31} \{12,19,31\} {12,19,31}\newline{10,25,37} \{10,25,37\} {10,25,37}\newline{10,15,26} \{10,15,26\} {10,15,26}\newline{7,21,27} \{7,21,27\} {7,21,27}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{12,19,31\}$ $\newline$ $\{10,25,37\}$ $\newline$ $\{10,15,26\}$ $\newline$ $\{7,21,27\}$