Question

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

Answer 1

To determine whether three side lengths can form a triangle, we can use the Triangle Inequality Theorem. This theorem states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following conditions must be satisfied:

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

Let's denote the sides as follows:
- \( a = 6 \) cm
- \( b = 8 \) cm
- \( c = 10 \) cm

Now, we can check each condition:

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 side lengths of 6 cm, 8 cm, and 10 cm can indeed form a triangle.