Question

What number of triangles can be formed using the set of three side lengths below
11 inches, 15 inches, 6 inches
One unique triangle
Many triangles
no triangles

Answer 1

To determine whether a triangle can be formed with the given side lengths of 11 inches, 15 inches, and 6 inches, we can use the triangle inequality theorem. According to this theorem, for any three sides \(a\), \(b\), and \(c\) (where \(a\), \(b\), and \(c\) are the lengths of the sides), the following conditions must be satisfied:

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

Let's assign the sides as follows:
- \(a = 11\)
- \(b = 15\)
- \(c = 6\)

Now, we can check the inequalities:

1. \(11 + 15 > 6\) ⟹ \(26 > 6\) (true)
2. \(11 + 6 > 15\) ⟹ \(17 > 15\) (true)
3. \(15 + 6 > 11\) ⟹ \(21 > 11\) (true)

All three conditions are satisfied, which means that it is possible to form a triangle with the side lengths of 11 inches, 15 inches, and 6 inches.

Therefore, the answer is: **One unique triangle.**