Question

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

Let's check the three combinations:

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 of the triangle inequality are satisfied, the side lengths 6 cm, 8 cm, and 10 cm can indeed form a triangle.

Therefore, 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.**