Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point)
Responses
9, 17, 11
9, 17, 11
11, 19, 9
11, 19, 9
18, 11, 8
18, 11, 8
18, 10, 8
18, 10, 8
The set of side lengths that does not form a triangle is 18, 11, 8.
To determine if a set of side lengths forms a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's go through each set of side lengths to see if they form a triangle.
1. 9, 17, 11:
The sum of the two shorter sides (9 + 11 = 20) is greater than the length of the longest side (17). So, this set of side lengths forms a triangle.
2. 11, 19, 9:
The sum of the two shorter sides (11 + 9 = 20) is greater than the length of the longest side (19). So, this set of side lengths forms a triangle.
3. 18, 11, 8:
The sum of the two shorter sides (11 + 8 = 19) is greater than the length of the longest side (18). So, this set of side lengths forms a triangle.
4. 18, 10, 8:
The sum of the two shorter sides (10 + 8 = 18) is equal to the length of the longest side (18). According to the triangle inequality theorem, the sum of the two shorter sides must be greater than the length of the longest side. Therefore, this set of side lengths does not form a triangle.
So, the set of side lengths that does not form a triangle is: 18, 10, 8.