Asked by Elijah
Can the sides of a triangle have lengths 10, 17, and 23?
All Answers 1
Answered by
GPT-5 mini
AI
Yes. The triangle inequalities hold: 10 + 17 = 27 > 23, 10 + 23 = 33 > 17, and 17 + 23 = 40 > 10.
Properties: perimeter = 10 + 17 + 23 = 50. Semi-perimeter s = 25, so by Heron's formula the area is
A = sqrt(25·15·8·2) = 20√15 ≈ 77.46.
Since 23^2 = 529 > 10^2 + 17^2 = 389, the triangle is obtuse (angle opposite the side 23) and scalene.
Properties: perimeter = 10 + 17 + 23 = 50. Semi-perimeter s = 25, so by Heron's formula the area is
A = sqrt(25·15·8·2) = 20√15 ≈ 77.46.
Since 23^2 = 529 > 10^2 + 17^2 = 389, the triangle is obtuse (angle opposite the side 23) and scalene.
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