Which of the following sets of numbers could represent the three sides of a triangle? {15,26,41} {5,10,16} {13,27,40} {15,27,40}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {15,26,41}  {5,10,16}  {13,27,40}  {15,27,40}

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.Test First Set: Test the first set of numbers {15, 26, 41} to see if they satisfy the Triangle Inequality Theorem. Check if 15 + 26 > 41, which is 41 > 41. This is not true, so the set {15, 26, 41} cannot represent the sides of a triangle.Test Second Set: Test the second set of numbers {5, 10, 16} to see if they satisfy the Triangle Inequality Theorem. Check if 5 + 10 > 16, which is 15 > 16. This is not true, so the set {5, 10, 16} cannot represent the sides of a triangle.Test Third Set: Test the third set of numbers {13, 27, 40} to see if they satisfy the Triangle Inequality Theorem. Check if 13 + 27 > 40, which is 40 > 40. This is not true, so the set {13, 27, 40} cannot represent the sides of a triangle.Test Fourth Set: Test the fourth set of numbers {15, 27, 40} to see if they satisfy the Triangle Inequality Theorem. Check if 15 + 27 > 40, which is 42 > 40. This is true. Check if 15 + 40 > 27, which is 55 > 27. This is true. Check if 27 + 40 > 15, which is 67 > 15. This is true. Since all conditions of the Triangle Inequality Theorem are satisfied, the set {15, 27, 40} can represent the sides of a triangle.

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{15,26,41\}$ $\newline$ $\{5,10,16\}$ $\newline$ $\{13,27,40\}$ $\newline$ $\{15,27,40\}$

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Which of the following sets of numbers could represent the three sides of a triangle?\newline{15,26,41} \{15,26,41\} {15,26,41}\newline{5,10,16} \{5,10,16\} {5,10,16}\newline{13,27,40} \{13,27,40\} {13,27,40}\newline{15,27,40} \{15,27,40\} {15,27,40}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{15,26,41\}$ $\newline$ $\{5,10,16\}$ $\newline$ $\{13,27,40\}$ $\newline$ $\{15,27,40\}$