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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 will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.%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.%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%0ASkip to navigation%0D%0AItem%0D%0A1%0D%0A, Unattempted.%0D%0AItem%0D%0A2%0D%0A, Unattempted.%0D%0AItem%0D%0A3%0D%0A, Unattempted.%0D%0AItem%0D%0A4%0D%0A, Unattempted.%0D%0AItem%0D%0A5%0D%0A, Unattempted.

1 answer

To determine if three side lengths can form a triangle, we use the triangle inequality theorem. This theorem states that for any three side lengths \(a\), \(b\), and \(c\), the following conditions must be met:

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

In this case, the side lengths are 6 cm, 8 cm, and 10 cm. Let's check the conditions:

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

Since all three conditions are satisfied, the three side lengths of 6 cm, 8 cm, and 10 cm 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.