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11. Triangle ABC has side lengths 9, 12, and 16. Do the side lengths form a Pythagorean triple? Work: a. yes b. no A B C D E

11. Triangle ABC has side lengths 9, 12, and 16. Do the side lengths form a Pythagorean triple? Work: a. yes b. no A B C D E

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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### Question 11 **Triangle ABC has side lengths 9, 12, and 16. Do the side lengths form a Pythagorean triple?** --- ### Work: (Workspace for calculation) --- ### Options: a. yes b. no --- ### Explanation: To determine if the side lengths form a Pythagorean triple, we need to check if they satisfy the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the largest number (hypotenuse) and \(a\) and \(b\) are the other two sides. Given side lengths: - 9 - 12 - 16 (hypotenuse) Calculate: 1. \(9^2 + 12^2 = 81 + 144 = 225\) 2. \(16^2 = 256\) Since \(225 \neq 256\), the side lengths 9, 12, and 16 do **not** form a Pythagorean triple. --- ### Answer: **b. no**
Transcribed Image Text:### Question 11 **Triangle ABC has side lengths 9, 12, and 16. Do the side lengths form a Pythagorean triple?** --- ### Work: (Workspace for calculation) --- ### Options: a. yes b. no --- ### Explanation: To determine if the side lengths form a Pythagorean triple, we need to check if they satisfy the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the largest number (hypotenuse) and \(a\) and \(b\) are the other two sides. Given side lengths: - 9 - 12 - 16 (hypotenuse) Calculate: 1. \(9^2 + 12^2 = 81 + 144 = 225\) 2. \(16^2 = 256\) Since \(225 \neq 256\), the side lengths 9, 12, and 16 do **not** form a Pythagorean triple. --- ### Answer: **b. no**
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