Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point)
Options
18, 11, 8
11, 19, 9
18, 10, 8
9, 17, 11
The set of side lengths that does not form a triangle is:
18, 11, 8
To determine which set of side lengths does not form a triangle, we can apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each set of side lengths:
1) 18, 11, 8:
Here, the sum of the two smaller sides is 11 + 8 = 19, which is greater than the longest side (18). So, this set does form a triangle.
2) 11, 19, 9:
In this case, the sum of the two smaller sides is 11 + 9 = 20, which is greater than the longest side (19). Therefore, this set forms a triangle.
3) 18, 10, 8:
For this set, the sum of the two smaller sides is 10 + 8 = 18, which is equal to the longest side (18). While this meets the triangle inequality theorem, it forms a degenerate triangle, which is a triangle with collinear vertices. Therefore, this set still forms a triangle.
4) 9, 17, 11:
In this case, the sum of the two smaller sides is 9 + 11 = 20, which is equal to the longest side (17). Similar to the previous set, this forms a degenerate triangle.
So, the set of side lengths that does not form a triangle is:
9, 17, 11.
To determine which set of side lengths does not form a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check the options one by one using this theorem:
Option 1: 18, 11, 8
Here, 18 + 11 = 29, which is greater than 8. Additionally, 11 + 8 = 19, which is greater than 18. Finally, 18 + 8 = 26, which is greater than 11. Therefore, this set of side lengths (18, 11, 8) can form a triangle.
Option 2: 11, 19, 9
Using the triangle inequality theorem, we find that 11 + 9 = 20, which is greater than 19. Similarly, 11 + 19 = 30, which is greater than 9. Lastly, 19 + 9 = 28, which is greater than 11. Thus, this set of side lengths (11, 19, 9) can form a triangle.
Option 3: 18, 10, 8
By applying the triangle inequality theorem, we find that 18 + 10 = 28, which is greater than 8. Moreover, 18 + 8 = 26, which is greater than 10. However, 10 + 8 = 18, which is not greater than 18. Therefore, this set of side lengths (18, 10, 8) cannot form a triangle.
Option 4: 9, 17, 11
Applying the triangle inequality theorem, we determine that 9 + 11 = 20, which is greater than 17. Additionally, 9 + 17 = 26, which is greater than 11. Similarly, 17 + 11 = 28, which is greater than 9. Hence, this set of side lengths (9, 17, 11) can form a triangle.
In conclusion, the set of side lengths that does not form a triangle is option 3: 18, 10, 8 inches.