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Which of the following sets of numbers could represent the three sides of a triangle? O {4, 16, 21} O {9, 14, 20} Submit Answer O {11,14, 27} O {6, 14, 20}

Which of the following sets of numbers could represent the three sides of a triangle? O {4, 16, 21} O {9, 14, 20} Submit Answer O {11,14, 27} O {6, 14, 20}

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Identifying Valid Triangle Side Lengths #### Problem Statement: **Which of the following sets of numbers could represent the three sides of a triangle?** #### Choices: 1. {4, 16, 21} 2. {9, 14, 20} 3. {11, 14, 27} 4. {6, 14, 20} #### Submission: - There is a "Submit Answer" button present for the students to click after making their selection. ### Detailed Explanation: To determine which set of numbers can represent the sides of a triangle, we need to verify each set using the triangle inequality theorem. This theorem states that for any three sides \(a\), \(b\), and \(c\) of a triangle, the following conditions must be met: - \(a + b > c\) - \(a + c > b\) - \(b + c > a\) Let's examine each set: 1. **Set {4, 16, 21}** - \(4 + 16 > 21 \quad \Rightarrow \quad 20 > 21\) (False) - \(4 + 21 > 16 \quad \Rightarrow \quad 25 > 16\) (True) - \(16 + 21 > 4 \quad \Rightarrow \quad 37 > 4\) (True) - **Conclusion:** False (Cannot form a triangle) 2. **Set {9, 14, 20}** - \(9 + 14 > 20 \quad \Rightarrow \quad 23 > 20\) (True) - \(9 + 20 > 14 \quad \Rightarrow \quad 29 > 14\) (True) - \(14 + 20 > 9 \quad \Rightarrow \quad 34 > 9\) (True) - **Conclusion:** True (Can form a triangle) 3. **Set {11, 14, 27}** - \(11 + 14 > 27 \quad \Rightarrow \quad 25 > 27\) (False) - \(11 + 27 > 14 \quad \Rightarrow \quad 38 > 14\) (True) - \(14 + 27 > 11 \quad \Rightarrow \quad 41 > 11\
Transcribed Image Text:### Identifying Valid Triangle Side Lengths #### Problem Statement: **Which of the following sets of numbers could represent the three sides of a triangle?** #### Choices: 1. {4, 16, 21} 2. {9, 14, 20} 3. {11, 14, 27} 4. {6, 14, 20} #### Submission: - There is a "Submit Answer" button present for the students to click after making their selection. ### Detailed Explanation: To determine which set of numbers can represent the sides of a triangle, we need to verify each set using the triangle inequality theorem. This theorem states that for any three sides \(a\), \(b\), and \(c\) of a triangle, the following conditions must be met: - \(a + b > c\) - \(a + c > b\) - \(b + c > a\) Let's examine each set: 1. **Set {4, 16, 21}** - \(4 + 16 > 21 \quad \Rightarrow \quad 20 > 21\) (False) - \(4 + 21 > 16 \quad \Rightarrow \quad 25 > 16\) (True) - \(16 + 21 > 4 \quad \Rightarrow \quad 37 > 4\) (True) - **Conclusion:** False (Cannot form a triangle) 2. **Set {9, 14, 20}** - \(9 + 14 > 20 \quad \Rightarrow \quad 23 > 20\) (True) - \(9 + 20 > 14 \quad \Rightarrow \quad 29 > 14\) (True) - \(14 + 20 > 9 \quad \Rightarrow \quad 34 > 9\) (True) - **Conclusion:** True (Can form a triangle) 3. **Set {11, 14, 27}** - \(11 + 14 > 27 \quad \Rightarrow \quad 25 > 27\) (False) - \(11 + 27 > 14 \quad \Rightarrow \quad 38 > 14\) (True) - \(14 + 27 > 11 \quad \Rightarrow \quad 41 > 11\
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