Question

How many triangles can be formed with segments measuring 9.125 ft, 15.378 ft, and 24.503 ft?
Responses

none
none

one
one

more than one

Answer 1

To determine if a triangle can be formed with the given segment lengths (9.125 ft, 15.378 ft, and 24.503 ft), we can use the triangle inequality theorem. This theorem states that for any triangle with sides \(a\), \(b\), and \(c\), the following conditions must hold true:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let's assign the lengths:
- \(a = 9.125\) ft
- \(b = 15.378\) ft
- \(c = 24.503\) ft

Now, we can check the inequalities:

1. \(9.125 + 15.378 > 24.503\)
- \(24.503 > 24.503\) (False)

2. \(9.125 + 24.503 > 15.378\)
- \(33.628 > 15.378\) (True)

3. \(15.378 + 24.503 > 9.125\)
- \(39.881 > 9.125\) (True)

Since the first condition is false, the three segments cannot form a triangle.

Therefore, the answer is **none**.