Determine the number of triangles that can be formed with the given information.
a=1, b=5, c=4
To determine the number of triangles that can be formed with the given information, we need to apply the triangle inequality theorem.
The triangle inequality theorem states that for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we have a=1, b=5, and c=4. Let's check if the triangle inequality holds for this combination of side lengths:
1. a + b > c: 1 + 5 > 4, which is true.
2. b + c > a: 5 + 4 > 1, which is true.
3. a + c > b: 1 + 4 > 5, which is false.
Since the third condition is false, we cannot form a triangle with the given side lengths of a=1, b=5, and c=4.
Therefore, in this case, the number of triangles that can be formed is 0.