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 can apply the triangle inequality theorem. According to this theorem, in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we have three side lengths:
a = 1
b = 5
c = 4
We need to check if the sum of any two sides is greater than the third side for all possible combinations.
Combination 1: a + b > c
1 + 5 > 4
6 > 4
This condition is met.
Combination 2: a + c > b
1 + 4 > 5
5 > 5
This condition is not met.
Combination 3: b + c > a
5 + 4 > 1
9 > 1
This condition is met.
In order for a triangle to be formed, all three conditions must be met. From the combinations above, we can see that only combinations 1 and 3 satisfy the conditions for triangle inequality. Therefore, there are 2 triangles that can be formed with the given information.