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 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 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 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 less than the length of the third side.

Answer 1

To determine whether the three 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 to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check the inequalities:

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 will indeed form a triangle.

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