Given the side length of 4 cm, 5 cm, and 9 cm, how many distinct triangles can be formed
To determine how many distinct triangles can be formed with side lengths of 4 cm, 5 cm, and 9 cm, we need to consider the triangle inequality theorem.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's consider the three given side lengths:
1. 4 cm, 5 cm, and 9 cm
We can form a triangle with these side lengths if and only if the sum of the lengths of any two sides is greater than the length of the third side.
Checking for each combination of sides:
4 cm + 5 cm > 9 cm (True)
4 cm + 9 cm > 5 cm (True)
5 cm + 9 cm > 4 cm (True)
Since all three combinations satisfy the triangle inequality theorem, we can form a triangle with these side lengths.
Therefore, only one distinct triangle can be formed with side lengths of 4 cm, 5 cm, and 9 cm.