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:
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
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.
1 answer