Which three lengths CANNOT be the lengths of the sides of a triangle(1 point)
Responses
A. 8m, 9m, 10m
B. 17m, 4m, 10m
C. 7m, 7m, 13m
D.25m, 16m, 11m
Choose one answer
To determine whether three lengths can form a triangle, you must check the triangle inequality theorem. The theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. So, for three sides a, b, and c, the triangle inequality would require:
1. a + b > c
2. a + c > b
3. b + c > a
Let's check each option against the triangle inequality theorem:
A. 8m, 9m, 10m
- 8 + 9 > 10 (17 > 10) ✓
- 8 + 10 > 9 (18 > 9) ✓
- 9 + 10 > 8 (19 > 8) ✓
B. 17m, 4m, 10m
- 17 + 4 > 10 (21 > 10) ✓
- 17 + 10 > 4 (27 > 4) ✓
- 4 + 10 > 17 (14 is not greater than 17) ✗
C. 7m, 7m, 13m
- 7 + 7 > 13 (14 > 13) ✓
- 7 + 13 > 7 (20 > 7) ✓
- 7 + 13 > 7 (20 > 7) ✓
D. 25m, 16m, 11m
- 25 + 16 > 11 (41 > 11) ✓
- 25 + 11 > 16 (36 > 16) ✓
- 16 + 11 > 25 (27 > 25) ✓
Option B (17m, 4m, 10m) is the one that cannot be the lengths of the sides of a triangle because the sum of the two shorter sides (4m + 10m = 14m) is not greater than the length of the longest side (17m). Therefore, the correct answer is:
B. 17m, 4m, 10m