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Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.? acute, because 102+122>152 acute, because 122+152>102 obtuse, because 102+122>152 obtuse, because 122+152>102

Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.? acute, because 102+122>152 acute, because 122+152>102 obtuse, because 102+122>152 obtuse, because 122+152>102

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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**Triangle Classification Question** **Question:** Which classification *best* represents a triangle with side lengths 10 in., 12 in., and 15 in.? 1. acute, because \(10^2 + 12^2 > 15^2\) 2. acute, because \(12^2 + 15^2 > 10^2\) 3. obtuse, because \(10^2 + 12^2 < 15^2\) 4. obtuse, because \(12^2 + 15^2 > 10^2\) ### Explanation: To accurately determine the type of triangle formed by the side lengths given, one can use the Pythagorean theorem as a comparison method. - If \(a^2 + b^2 > c^2\), the triangle is acute. - If \(a^2 + b^2 < c^2\), the triangle is obtuse. - If \(a^2 + b^2 = c^2\), the triangle is right. Given: - Side lengths: 10 in., 12 in., 15 in. Check: - \(10^2 + 12^2 = 100 + 144 = 244\) - \(15^2 = 225\) Since \(244 > 225\), option 1 is correct. The triangle is acute, because \(10^2 + 12^2 > 15^2\).
Transcribed Image Text:**Triangle Classification Question** **Question:** Which classification *best* represents a triangle with side lengths 10 in., 12 in., and 15 in.? 1. acute, because \(10^2 + 12^2 > 15^2\) 2. acute, because \(12^2 + 15^2 > 10^2\) 3. obtuse, because \(10^2 + 12^2 < 15^2\) 4. obtuse, because \(12^2 + 15^2 > 10^2\) ### Explanation: To accurately determine the type of triangle formed by the side lengths given, one can use the Pythagorean theorem as a comparison method. - If \(a^2 + b^2 > c^2\), the triangle is acute. - If \(a^2 + b^2 < c^2\), the triangle is obtuse. - If \(a^2 + b^2 = c^2\), the triangle is right. Given: - Side lengths: 10 in., 12 in., 15 in. Check: - \(10^2 + 12^2 = 100 + 144 = 244\) - \(15^2 = 225\) Since \(244 > 225\), option 1 is correct. The triangle is acute, because \(10^2 + 12^2 > 15^2\).
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