Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point)

Question

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 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.
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.

Answer 1

To determine if three side lengths can form a triangle, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check the side lengths 6 cm, 8 cm, and 10 cm:

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, these three side lengths 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.