Question

Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point)%0D%0AResponses%0D%0A%0D%0AThey cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.%0D%0AThey cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.%0D%0A%0D%0AThey will form a triangle because the sum of any two of the side lengths is less than the length of the third side.%0D%0AThey will form a triangle because the sum of any two of the side lengths is less than the length of the third side.%0D%0A%0D%0AThey cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side.%0D%0AThey cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side.%0D%0A%0D%0AThey 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 whether the given side lengths (6 cm, 8 cm, and 10 cm) will form a triangle, we can use the triangle inequality theorem. This theorem states that for any three lengths 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 conditions:

1. \(6 + 8 > 10\)
   \(14 > 10\) (True)

2. \(6 + 10 > 8\)
   \(16 > 8\) (True)

3. \(8 + 10 > 6\)
   \(18 > 6\) (True)

Since all conditions of the triangle inequality theorem are satisfied, these 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.