Which of the following sets of numbers could represent the three sides of a triangle? {10,13,22} {14,26,42} {6,14,22} {15,18,34}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {10,13,22}  {14,26,42}  {6,14,22}  {15,18,34}

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 {10,13,22}: Apply the Triangle Inequality Theorem to the first set {10,13,22}. Check if 10 + 13 > 22, 10 + 22 > 13, and 13 + 22 > 10. Calculation: 10 + 13 = 23, 10 + 22 = 32, 13 + 22 = 35. 23 > 22 (True), 32 > 13 (True), but 35 > 10 (True). However, the first condition 10 + 13 > 22 is not satisfied, so this set cannot represent the sides of a triangle.Apply Theorem to Set {14,26,42}: Apply the Triangle Inequality Theorem to the second set {14,26,42}. Check if 14 + 26 > 42, 14 + 42 > 26, and 26 + 42 > 14. Calculation: 14 + 26 = 40, 14 + 42 = 56, 26 + 42 = 68. 40 > 42 (False), 56 > 26 (True), and 68 > 14 (True). The first condition 14 + 26 > 42 is not satisfied, so this set cannot represent the sides of a triangle.Apply Theorem to Set {6,14,22}: Apply the Triangle Inequality Theorem to the third set {6,14,22}. Check if 6 + 14 > 22, 6 + 22 > 14, and 14 + 22 > 6. Calculation: 6 + 14 = 20, 6 + 22 = 28, 14 + 22 = 36. 20 > 22 (False), 28 > 14 (True), and 36 > 6 (True). The first condition 6 + 14 > 22 is not satisfied, so this set cannot represent the sides of a triangle.Apply Theorem to Set {15,18,34}: Apply the Triangle Inequality Theorem to the fourth set {15,18,34}. Check if 15 + 18 > 34, 15 + 34 > 18, and 18 + 34 > 15. Calculation: 15 + 18 = 33, 15 + 34 = 49, 18 + 34 = 52. 33 > 34 (False), 49 > 18 (True), and 52 > 15 (True). The first condition 15 + 18 > 34 is not satisfied, so this set cannot represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{10,13,22\}$ $\newline$ $\{14,26,42\}$ $\newline$ $\{6,14,22\}$ $\newline$ $\{15,18,34\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{10,13,22} \{10,13,22\} {10,13,22}\newline{14,26,42} \{14,26,42\} {14,26,42}\newline{6,14,22} \{6,14,22\} {6,14,22}\newline{15,18,34} \{15,18,34\} {15,18,34}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{10,13,22\}$ $\newline$ $\{14,26,42\}$ $\newline$ $\{6,14,22\}$ $\newline$ $\{15,18,34\}$