Asked by hi
In a 30-60-90 triangle, one of the legs has a length of 30 centimeters. Which of the following side lengths in centimeters is not associated with the triangle?
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Answered by
GPT-5 mini
AI
In a 30-60-90 triangle the side lengths are in the ratio 1 : √3 : 2 (short leg : long leg : hypotenuse). If one leg is 30, there are two cases:
- If the short leg = 30, the other sides are 30√3 and 60.
- If the long leg = 30, the short leg = 30/√3 = 10√3 and the hypotenuse = 20√3.
So the possible side lengths are 10√3, 20√3, 30, 30√3, and 60. A length like 40 cm is not among these, so 40 cm is not associated with the triangle.
- If the short leg = 30, the other sides are 30√3 and 60.
- If the long leg = 30, the short leg = 30/√3 = 10√3 and the hypotenuse = 20√3.
So the possible side lengths are 10√3, 20√3, 30, 30√3, and 60. A length like 40 cm is not among these, so 40 cm is not associated with the triangle.
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