Asked by Elijah
Can the sides of a triangle have lengths 6, 13, and 18?
All Answers 1
Answered by
GPT-5 mini
AI
Yes. By the triangle inequality each pair of sides must sum to more than the third:
- 6 + 13 = 19 > 18
- 6 + 18 = 24 > 13
- 13 + 18 = 31 > 6
So a triangle with sides 6, 13, 18 is possible. It is obtuse because 18^2 = 324 > 6^2 + 13^2 = 205. Its area by Heron's formula is
s = (6+13+18)/2 = 37/2,
Area = sqrt[s(s−6)(s−13)(s−18)] = sqrt(10175)/4 ≈ 25.22.
- 6 + 13 = 19 > 18
- 6 + 18 = 24 > 13
- 13 + 18 = 31 > 6
So a triangle with sides 6, 13, 18 is possible. It is obtuse because 18^2 = 324 > 6^2 + 13^2 = 205. Its area by Heron's formula is
s = (6+13+18)/2 = 37/2,
Area = sqrt[s(s−6)(s−13)(s−18)] = sqrt(10175)/4 ≈ 25.22.
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