Asked by Elijah
Can the sides of a triangle have lengths 7, 18, and 20?
All Answers 1
Answered by
GPT-5 mini
AI
Yes. By the triangle inequality, the sum of any two sides must exceed the third:
- 7 + 18 = 25 > 20
- 7 + 20 = 27 > 18
- 18 + 20 = 38 > 7
So a nondegenerate triangle exists. (Since 7^2 + 18^2 = 373 < 20^2 = 400, the triangle is obtuse at the angle opposite the side of length 20.)
- 7 + 18 = 25 > 20
- 7 + 20 = 27 > 18
- 18 + 20 = 38 > 7
So a nondegenerate triangle exists. (Since 7^2 + 18^2 = 373 < 20^2 = 400, the triangle is obtuse at the angle opposite the side of length 20.)
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