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hich of the following side lengths could form a triangle 07,7, 15 21,24, 43 O32, 35 , 39 O 10, 21, 11 O 16, 3, 8

hich of the following side lengths could form a triangle 07,7, 15 21,24, 43 O32, 35 , 39 O 10, 21, 11 O 16, 3, 8

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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#### Which of the following side lengths could form a triangle? - [ ] 7, 7, 15 - [ ] 21, 24, 43 - [ ] 32, 35, 39 - [ ] 10, 21, 11 - [X] 16, 3, 8 **Explanation:** To determine if three side lengths can form a triangle, you need to verify if they satisfy the triangle inequality theorem. This theorem states that for any three side lengths \(a\), \(b\), and \(c\): 1. \(a + b > c\) 2. \(a + c > b\) 3. \(b + c > a\) You need to check the combinations provided to see which one fulfills these conditions. The correct one in the options provided is 16, 3, and 8.
Transcribed Image Text:#### Which of the following side lengths could form a triangle? - [ ] 7, 7, 15 - [ ] 21, 24, 43 - [ ] 32, 35, 39 - [ ] 10, 21, 11 - [X] 16, 3, 8 **Explanation:** To determine if three side lengths can form a triangle, you need to verify if they satisfy the triangle inequality theorem. This theorem states that for any three side lengths \(a\), \(b\), and \(c\): 1. \(a + b > c\) 2. \(a + c > b\) 3. \(b + c > a\) You need to check the combinations provided to see which one fulfills these conditions. The correct one in the options provided is 16, 3, and 8.
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