Which three lengths CANNOT be the lengths of the sides of a triangle(1 point)
Responses
8m, 9m, 10m
17m, 4m, 10m
7m, 7m, 13m
25m, 16m, 11m
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Therefore, we can use this rule to determine which sets of side lengths cannot form a triangle.
Let's check each provided set of lengths:
1. 8m, 9m, 10m:
Checking the triangle inequality for each pair:
8 + 9 > 10
9 + 10 > 8
8 + 10 > 9
All inequalities are true, so these lengths can form a triangle.
2. 17m, 4m, 10m:
Checking the triangle inequality for each pair:
17 + 4 > 10
17 + 10 > 4
4 + 10 > 17, this is not true (14 is not greater than 17)
Therefore, these lengths cannot form a triangle.
3. 7m, 7m, 13m:
Checking the triangle inequality for each pair:
7 + 7 > 13 (this is true, 14 > 13)
7 + 13 > 7 (obviously true)
7 + 13 > 7 (obviously true)
All inequalities are satisfied, so these lengths can form a triangle.
4. 25m, 16m, 11m:
Checking the triangle inequality for each pair:
25 + 16 > 11 (this is true)
25 + 11 > 16 (this is true)
16 + 11 > 25, this is not true (27 is not greater than 25)
So, these lengths cannot form a triangle.
The sets of lengths that cannot form a triangle according to the Triangle Inequality Theorem are:
- 17m, 4m, 10m
- 25m, 16m, 11m