Which of the following sets of numbers could represent the three sides of a triangle? {12,20,34} {4,6,11} {10,12,21} {13,18,33}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {12,20,34}  {4,6,11}  {10,12,21}  {13,18,33}

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 {12, 20, 34}: Apply the Triangle Inequality Theorem to the first set of numbers {12, 20, 34}. Check if the sum of any two numbers is greater than the third number. 12 + 20 = 32, which is not greater than 34.Set {12, 20, 34} Analysis: Since 32 is not greater than 34, the set {12, 20, 34} does not satisfy the Triangle Inequality Theorem and cannot represent the sides of a triangle.Apply Theorem to Set {4, 6, 11}: Apply the Triangle Inequality Theorem to the second set of numbers {4, 6, 11}. Check if the sum of any two numbers is greater than the third number. 4 + 6 = 10, which is not greater than 11.Set {4, 6, 11} Analysis: Since 10 is not greater than 11, the set {4, 6, 11} does not satisfy the Triangle Inequality Theorem and cannot represent the sides of a triangle.Apply Theorem to Set {10, 12, 21}: Apply the Triangle Inequality Theorem to the third set of numbers {10, 12, 21}. Check if the sum of any two numbers is greater than the third number. 10 + 12 = 22, which is greater than 21.Set {10, 12, 21} Analysis: Check the other two combinations for the set {10, 12, 21} to ensure all conditions of the Triangle Inequality Theorem are met. 10 + 21 = 31, which is greater than 12. 12 + 21 = 33, which is greater than 10.Apply Theorem to Set {13, 18, 33}: Since all combinations of the set {10, 12, 21} satisfy the Triangle Inequality Theorem, this set can represent the sides of a triangle.Set {13, 18, 33} Analysis: Apply the Triangle Inequality Theorem to the fourth set of numbers {13, 18, 33}. Check if the sum of any two numbers is greater than the third number. 13 + 18 = 31, which is not greater than 33.Since 31 is not greater than 33, the set {13, 18, 33} does not satisfy the Triangle Inequality Theorem and cannot represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{12,20,34\}$ $\newline$ $\{4,6,11\}$ $\newline$ $\{10,12,21\}$ $\newline$ $\{13,18,33\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{12,20,34} \{12,20,34\} {12,20,34}\newline{4,6,11} \{4,6,11\} {4,6,11}\newline{10,12,21} \{10,12,21\} {10,12,21}\newline{13,18,33} \{13,18,33\} {13,18,33}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{12,20,34\}$ $\newline$ $\{4,6,11\}$ $\newline$ $\{10,12,21\}$ $\newline$ $\{13,18,33\}$