Question

Determine whether these three side lengths will from a triangle: 6 cm, 8 cm, and 10 cm.
A. They will form a triangle because the sum of any two of the side lengths is less than the length of the third side.
B. They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side
C. They cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side
D. They will form a triangle because the sum of any two of the side lengths is greater that the length of the third side

Answer 1

To determine whether the three side lengths (6 cm, 8 cm, and 10 cm) can form a triangle, we can use the triangle inequality theorem. According to this theorem, for any three sides \(a\), \(b\), and \(c\) of a triangle, the following must be true:

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

Let's assign the sides:
- \(a = 6\)
- \(b = 8\)
- \(c = 10\)

Now check the inequalities:

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

Since all three inequalities are satisfied, the side lengths can indeed form a triangle.

The correct answer is:
**D. They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.**