Sides of a Triangle Quick Check 1 of 51 of 5 Items Question Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point) Responses 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 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. Skip to navigation page 15 of 15

Answer 1

To determine whether the side lengths of 6 cm, 8 cm, and 10 cm can form a triangle, we can apply the triangle inequality theorem. This theorem states that for any three sides of 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 three conditions are satisfied, the three side lengths can 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.