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 check if the sum of the lengths of any two sides of the triangle is greater than the length of the remaining side.
Let's use the triangle inequality theorem to check this condition.
According to the theorem, for any triangle with sides a, b, and c:
a + b > c
a + c > b
b + c > a
Let's apply this to the given information:
a=1, b=5, c=4
a + b > c: 1 + 5 = 6 > 4 (True)
a + c > b: 1 + 4 = 5 > 5 (False)
b + c > a: 5 + 4 = 9 > 1 (True)
Based on these results, we see that the second condition (a + c > b) is not satisfied. Therefore, we cannot form a triangle with the given side lengths.
In conclusion, in this case, no triangles can be formed with the side lengths a=1, b=5, and c=4.