Question

Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses
A. 8, 8, 20,
B. 20, 10, 30
C. 8, 4, 12
D. 10, 20, 15

Answer 1

To determine which set of side lengths can form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following inequalities must hold:

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

We will check each of the provided options:

**A. 8, 8, 20**
- \(8 + 8 > 20\) (False)
- \(8 + 20 > 8\) (True)
- \(8 + 20 > 8\) (True)

Not a triangle.

**B. 20, 10, 30**
- \(20 + 10 > 30\) (False)
- \(20 + 30 > 10\) (True)
- \(10 + 30 > 20\) (True)

Not a triangle.

**C. 8, 4, 12**
- \(8 + 4 > 12\) (False)
- \(8 + 12 > 4\) (True)
- \(4 + 12 > 8\) (True)

Not a triangle.

**D. 10, 20, 15**
- \(10 + 20 > 15\) (True)
- \(10 + 15 > 20\) (False)
- \(20 + 15 > 10\) (True)

Not a triangle.

After checking all the options, none of the sets of lengths can form a triangle based on the Triangle Inequality Theorem.