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

Question

Responses which is the true correct response

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 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.

Answer 1

To determine whether the three side lengths (6 cm, 8 cm, and 10 cm) will form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for any three sides \( a \), \( b \), and \( c \) of a triangle, the following conditions must be met:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

Let's check these conditions for the sides 6 cm, 8 cm, and 10 cm:

1. \( 6 + 8 = 14 > 10 \) (True)
2. \( 6 + 10 = 16 > 8 \) (True)
3. \( 8 + 10 = 18 > 6 \) (True)

Since all three conditions are satisfied, these side lengths will 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.