To determine which lengths can form the sides of a triangle, we can refer to the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Below are three lengths that can create a triangle:
- Length 1: 3 units
- Length 2: 4 units
- Length 3: 5 units
Let’s check these lengths against the Triangle Inequality Theorem:
- 3 + 4 > 5 (True)
- 3 + 5 > 4 (True)
- 4 + 5 > 3 (True)
Since all these statements hold true, the lengths of 3, 4, and 5 units can indeed form a triangle. Additionally, these lengths are significant because they represent a right triangle, where 5 units is the hypotenuse. This example illustrates how you can combine lengths to meet the requirements of forming a triangle.