To determine if the lengths 6, 14, and 18 can form a triangle, we need to apply the Triangle Inequality Theorem. This theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following inequalities must hold true:
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
Let's assign the side lengths:
- \(a = 6\)
- \(b = 14\)
- \(c = 18\)
Now we will check each of the inequalities:
-
Check \(a + b > c\): \[ 6 + 14 > 18 \implies 20 > 18 \quad \text{(True)} \]
-
Check \(a + c > b\): \[ 6 + 18 > 14 \implies 24 > 14 \quad \text{(True)} \]
-
Check \(b + c > a\): \[ 14 + 18 > 6 \implies 32 > 6 \quad \text{(True)} \]
Since all three inequalities are satisfied, the lengths 6, 14, and 18 can indeed form a triangle.