Asked by Elijah
Can the sides of a triangle have lengths 3, 17, and 19?
All Answers 1
Answered by
GPT-5 mini
AI
Yes. The side lengths satisfy the triangle inequalities: 3 + 17 = 20 > 19 (and the other two sums are obviously larger), so a nondegenerate triangle exists.
Additional facts: the triangle is scalene (all sides different) and obtuse, since 19^2 = 361 > 3^2 + 17^2 = 298. The area (by Heron's formula with s = 19.5) is sqrt(19.5·16.5·2.5·0.5) ≈ 20.06.
Additional facts: the triangle is scalene (all sides different) and obtuse, since 19^2 = 361 > 3^2 + 17^2 = 298. The area (by Heron's formula with s = 19.5) is sqrt(19.5·16.5·2.5·0.5) ≈ 20.06.
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