To determine if the given side lengths can form a triangle, you can apply the triangle inequality theorem. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Given the side lengths:
- a = 10.6 cm
- b = 5.6 cm
- c = 4.0 cm
We must check if these three conditions are satisfied:
1. a + b > c
2. a + c > b
3. b + c > a
Let's check each condition:
1. 10.6 cm + 5.6 cm > 4.0 cm
16.2 cm > 4.0 cm (True)
2. 10.6 cm + 4.0 cm > 5.6 cm
14.6 cm > 5.6 cm (True)
3. 5.6 cm + 4.0 cm > 10.6 cm
9.6 cm > 10.6 cm (False)
The third condition is not satisfied, which means that the given side lengths cannot form a triangle, because the sum of the two shorter sides (5.6 cm and 4.0 cm) is not greater than the length of the longest side (10.6 cm).
could 10.6 cm, 5.6 cm, and 4.0 cm, be the side of lengths triangle?
1 answer