Question

Which choice shows three lengths that cannot be the lengths of the three sides of a triangle?
A
2 cm, 8 cm, 8 cm
B
2 cm, 3cm, 6 cm
C
4 cm, 5 cm, 7 cm
D
5 cm, 6 cm, 9 cm

Answer 1

To determine which choice shows three lengths that cannot be the lengths of the three sides of a triangle, we can use the triangle inequality theorem. This theorem states that for three lengths \( a \), \( b \), and \( c \) to form a triangle, the following conditions must hold:

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

Let's analyze each option:

A. **2 cm, 8 cm, 8 cm**
- \( 2 + 8 = 10 > 8 \) (true)
- \( 2 + 8 = 10 > 8 \) (true)
- \( 8 + 8 = 16 > 2 \) (true)
- The sides can form a triangle.

B. **2 cm, 3 cm, 6 cm**
- \( 2 + 3 = 5 < 6 \) (false)
- The sides cannot form a triangle.

C. **4 cm, 5 cm, 7 cm**
- \( 4 + 5 = 9 > 7 \) (true)
- \( 4 + 7 = 11 > 5 \) (true)
- \( 5 + 7 = 12 > 4 \) (true)
- The sides can form a triangle.

D. **5 cm, 6 cm, 9 cm**
- \( 5 + 6 = 11 > 9 \) (true)
- \( 5 + 9 = 14 > 6 \) (true)
- \( 6 + 9 = 15 > 5 \) (true)
- The sides can form a triangle.

Based on this analysis, the choice that shows three lengths that cannot be the lengths of the three sides of a triangle is:

**B. 2 cm, 3 cm, 6 cm**.