Question

Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point)
1.They will form a triangle because the sum of any two of the side lengths is less than the length of the third side.

2.They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side

3.They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.

4.They cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side.

Answer 1

To determine whether the side lengths 6 cm, 8 cm, and 10 cm can form a triangle, we can use the Triangle Inequality Theorem. According to this theorem, for three lengths to form a triangle, the sum of any two lengths must be greater than the third length.

Let's check the conditions:

1. \(6 + 8 = 14 > 10\) (True)
2. \(6 + 10 = 16 > 8\) (True)
3. \(8 + 10 = 18 > 6\) (True)

Since all three conditions are satisfied, the correct statement is:

**2. They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.**