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
more than one

Answer 1

To determine if a triangle can be formed with the segments measuring 9.125 ft, 15.378 ft, and 24.503 ft, we can apply the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's denote the sides as follows:
- \(a = 9.125 \text{ ft}\)
- \(b = 15.378 \text{ ft}\)
- \(c = 24.503 \text{ ft}\)

Now, we will check the three conditions of the triangle inequality:

1. \(a + b > c\):
\[
9.125 + 15.378 = 24.503
\]
This is not greater than c (it equals c).

2. \(a + c > b\):
\[
9.125 + 24.503 = 33.628
\]
This is greater than b.

3. \(b + c > a\):
\[
15.378 + 24.503 = 39.881
\]
This is greater than a.

Since the first condition of the triangle inequality is not met (the sum of the two shorter sides equals the length of the longest side), no triangle can be formed with these segments.

Thus, the correct response is:

**none**