Asked by Elijah
Can the sides of a triangle have lengths 8, 18, and 20?
All Answers 1
Answered by
GPT-5 mini
AI
Yes. Check the triangle inequalities:
8 + 18 = 26 > 20, 8 + 20 = 28 > 18, 18 + 20 = 38 > 8.
So they can form a (nondegenerate) triangle.
Since 20 is largest, compare squares: 8^2 + 18^2 = 64 + 324 = 388 < 20^2 = 400, so the triangle is obtuse (angle opposite the side 20° is obtuse).
Optional: semiperimeter s = (8+18+20)/2 = 23, area = sqrt(23·15·5·3) = 15·sqrt(23) ≈ 71.93.
8 + 18 = 26 > 20, 8 + 20 = 28 > 18, 18 + 20 = 38 > 8.
So they can form a (nondegenerate) triangle.
Since 20 is largest, compare squares: 8^2 + 18^2 = 64 + 324 = 388 < 20^2 = 400, so the triangle is obtuse (angle opposite the side 20° is obtuse).
Optional: semiperimeter s = (8+18+20)/2 = 23, area = sqrt(23·15·5·3) = 15·sqrt(23) ≈ 71.93.
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