Which of the following sets of numbers could represent the three sides of a triangle? {9,11,20} {13,15,28} {15,29,43} {9,21,30}

Question

Which of the following sets of numbers could represent the three sides of a triangle?  {9,11,20}  {13,15,28}  {15,29,43}  {9,21,30}

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.Check First Set: Check the first set of numbers {9,11,20} to see if they satisfy the Triangle Inequality Theorem. We need to check if 9 + 11 > 20, 9 + 20 > 11, and 11 + 20 > 9.Perform Calculations First Set: Perform the calculations for the first set. 9 + 11 = 20, which is not greater than 20. Therefore, the first set {9,11,20} does not satisfy the Triangle Inequality Theorem and cannot represent the sides of a triangle.Check Second Set: Check the second set of numbers {13,15,28} to see if they satisfy the Triangle Inequality Theorem. We need to check if 13 + 15 > 28, 13 + 28 > 15, and 15 + 28 > 13.Perform Calculations Second Set: Perform the calculations for the second set. 13 + 15 = 28, which is not greater than 28. Therefore, the second set {13,15,28} does not satisfy the Triangle Inequality Theorem and cannot represent the sides of a triangle.Check Third Set: Check the third set of numbers {15,29,43} to see if they satisfy the Triangle Inequality Theorem. We need to check if 15 + 29 > 43, 15 + 43 > 29, and 29 + 43 > 15.Perform Calculations Third Set: Perform the calculations for the third set. 15 + 29 = 44, which is greater than 43. 15 + 43 = 58, which is greater than 29. 29 + 43 = 72, which is greater than 15. Therefore, the third set {15,29,43} satisfies the Triangle Inequality Theorem and could represent the sides of a triangle.Check Fourth Set: There is no need to check the fourth set {9,21,30} because we have already found a set that satisfies the Triangle Inequality Theorem. However, for completeness, let's check it. We need to check if 9 + 21 > 30, 9 + 30 > 21, and 21 + 30 > 9.Perform Calculations Fourth Set: Perform the calculations for the fourth set. 9 + 21 = 30, which is not greater than 30. Therefore, the fourth set {9,21,30} 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? $\newline$ $\{9,11,20\}$ $\newline$ $\{13,15,28\}$ $\newline$ $\{15,29,43\}$ $\newline$ $\{9,21,30\}$

Full solution

More problems from Checkpoint: Rational and irrational numbers

Related topics

Which of the following sets of numbers could represent the three sides of a triangle?\newline{9,11,20} \{9,11,20\} {9,11,20}\newline{13,15,28} \{13,15,28\} {13,15,28}\newline{15,29,43} \{15,29,43\} {15,29,43}\newline{9,21,30} \{9,21,30\} {9,21,30}

Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{9,11,20\}$ $\newline$ $\{13,15,28\}$ $\newline$ $\{15,29,43\}$ $\newline$ $\{9,21,30\}$