To determine whether three lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following conditions must be satisfied:
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
Given the lengths 5, 1, and 4, we can let \(a = 5\), \(b = 1\), and \(c = 4\). Now, we will check each of the triangle inequality conditions:
-
\(a + b > c\) \[ 5 + 1 > 4 \quad \text{(6 > 4, which is true)} \]
-
\(a + c > b\) \[ 5 + 4 > 1 \quad \text{(9 > 1, which is true)} \]
-
\(b + c > a\) \[ 1 + 4 > 5 \quad \text{(5 > 5, which is false)} \]
Since the third condition (\(b + c > a\)) is not satisfied, the lengths 5, 1, and 4 cannot form a triangle. Thus, the answer is no.
1 answer