Which of the following sets of numbers could represent the three sides of a triangle? {13,22,32} {11,22,33} {14,20,36} {15,21,37}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {13,22,32}  {11,22,33}  {14,20,36}  {15,21,37}

Bytelearn · Accepted Answer

Recall Triangle Inequality Theorem: Recall the Triangle Inequality Theorem. The Triangle Inequality Theorem 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 {13,22,32}: Apply the Triangle Inequality Theorem to the first set {13,22,32}. Check if 13 + 22 > 32, 13 + 32 > 22, and 22 + 32 > 13. 13 + 22 = 35, which is greater than 32. 13 + 32 = 45, which is greater than 22. 22 + 32 = 54, which is greater than 13. All conditions are satisfied, so {13,22,32} could represent the sides of a triangle.Apply Theorem to Set {11,22,33}: Apply the Triangle Inequality Theorem to the second set {11,22,33}. Check if 11 + 22 > 33, 11 + 33 > 22, and 22 + 33 > 11. 11 + 22 = 33, which is not greater than 33. This set does not satisfy the Triangle Inequality Theorem, so {11,22,33} cannot represent the sides of a triangle.Apply Theorem to Set {14,20,36}: Apply the Triangle Inequality Theorem to the third set {14,20,36}. Check if 14 + 20 > 36, 14 + 36 > 20, and 20 + 36 > 14. 14 + 20 = 34, which is not greater than 36. This set does not satisfy the Triangle Inequality Theorem, so {14,20,36} cannot represent the sides of a triangle.Apply Theorem to Set {15,21,37}: Apply the Triangle Inequality Theorem to the fourth set {15,21,37}. Check if 15 + 21 > 37, 15 + 37 > 21, and 21 + 37 > 15. 15 + 21 = 36, which is not greater than 37. This set does not satisfy the Triangle Inequality Theorem, so {15,21,37} cannot represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{13,22,32\}$ $\newline$ $\{11,22,33\}$ $\newline$ $\{14,20,36\}$ $\newline$ $\{15,21,37\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{13,22,32} \{13,22,32\} {13,22,32}\newline{11,22,33} \{11,22,33\} {11,22,33}\newline{14,20,36} \{14,20,36\} {14,20,36}\newline{15,21,37} \{15,21,37\} {15,21,37}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{13,22,32\}$ $\newline$ $\{11,22,33\}$ $\newline$ $\{14,20,36\}$ $\newline$ $\{15,21,37\}$