Question

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?

Multiple Choice Answers
10, square root of, 3, end square root10
3
​

20, square root of, 3, end square root20
3
​

30, square root of, 3, end square root30
3
​

60, square root of, 3, end square root60
3

Answer 1

In a 30-60-90 triangle the sides are in ratio 1 : √3 : 2 (short leg : long leg : hypotenuse). If one leg is 30, it is either the short leg or the long leg.

- If the short leg = 30, the long leg = 30√3 and the hypotenuse = 60.
- If the long leg = 30, the short leg = 30/√3 = 10√3 and the hypotenuse = 20√3.

Thus the √3-containing side lengths that can occur are 10√3, 20√3, and 30√3. 60√3 cannot occur. So the answer is 60√3.