Which of the following sets of numbers could not represent the three sides of a triangle? {10,12,19} {15,27,39} {10,15,22} {12,18,32}

Question

Which of the following sets of numbers could not represent the three sides of a triangle?  {10,12,19}  {15,27,39}  {10,15,22}  {12,18,32}

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 {10,12,19}: Apply the Triangle Inequality Theorem to the first set {10,12,19}. Check if 10 + 12 > 19, 10 + 19 > 12, and 12 + 19 > 10. 10 + 12 = 22, which is greater than 19. 10 + 19 = 29, which is greater than 12. 12 + 19 = 31, which is greater than 10. All conditions are satisfied, so {10,12,19} could represent the sides of a triangle.Apply Theorem to {15,27,39}: Apply the Triangle Inequality Theorem to the second set {15,27,39}. Check if 15 + 27 > 39, 15 + 39 > 27, and 27 + 39 > 15. 15 + 27 = 42, which is greater than 39. 15 + 39 = 54, which is greater than 27. 27 + 39 = 66, which is greater than 15. All conditions are satisfied, so {15,27,39} could represent the sides of a triangle.Apply Theorem to {10,15,22}: Apply the Triangle Inequality Theorem to the third set {10,15,22}. Check if 10 + 15 > 22, 10 + 22 > 15, and 15 + 22 > 10. 10 + 15 = 25, which is greater than 22. 10 + 22 = 32, which is greater than 15. 15 + 22 = 37, which is greater than 10. All conditions are satisfied, so {10,15,22} could represent the sides of a triangle.Apply Theorem to {12,18,32}: Apply the Triangle Inequality Theorem to the fourth set {12,18,32}. Check if 12 + 18 > 32, 12 + 32 > 18, and 18 + 32 > 12. 12 + 18 = 30, which is not greater than 32. 12 + 32 = 44, which is greater than 18. 18 + 32 = 50, which is greater than 12. The first condition is not satisfied, so {12,18,32} could not represent the sides of a triangle.

Which of the following sets of numbers could not represent the three sides of a triangle? $\newline$ $\{10,12,19\}$ $\newline$ $\{15,27,39\}$ $\newline$ $\{10,15,22\}$ $\newline$ $\{12,18,32\}$

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Which of the following sets of numbers could not represent the three sides of a triangle?\newline{10,12,19} \{10,12,19\} {10,12,19}\newline{15,27,39} \{15,27,39\} {15,27,39}\newline{10,15,22} \{10,15,22\} {10,15,22}\newline{12,18,32} \{12,18,32\} {12,18,32}

Which of the following sets of numbers could not represent the three sides of a triangle? $\newline$ $\{10,12,19\}$ $\newline$ $\{15,27,39\}$ $\newline$ $\{10,15,22\}$ $\newline$ $\{12,18,32\}$