Question

Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point) Responses They will form a triangle because the sum of any two of the side lengths is less than the length of the third side. They will form a triangle because the sum of any two of the side lengths is less than the length of the third side. They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side. They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side. They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side. They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side. 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. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check all three conditions:

1. \(6 + 8 > 10\)
- \(14 > 10\) (True)

2. \(6 + 10 > 8\)
- \(16 > 8\) (True)

3. \(8 + 10 > 6\)
- \(18 > 6\) (True)

Since all three conditions are satisfied, the side lengths 6 cm, 8 cm, and 10 cm can indeed form a triangle.

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