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.

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

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 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.

Answer 3

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.

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

Let's check if this condition is satisfied:

1. The sum of the first two side lengths is 6 cm + 8 cm = 14 cm. This is greater than the length of the third side, which is 10 cm.
2. The sum of the first and third side lengths is 6 cm + 10 cm = 16 cm. Again, this is greater than the second side length, which is 8 cm.
3. Finally, the sum of the second and third side lengths is 8 cm + 10 cm = 18 cm. Once again, this is greater than the first side length, which is 6 cm.

Since the sum of any two side lengths is greater than the length of the third side, we can conclude that these side lengths will form a triangle.