Answer:
A: Yes, B: No, C: Yes, D: Yes, E: Yes
A: No, B: Yes, C: No, D: No, E: Yes
17: 2 < x < 24
18: 1 < x < 69
19: 7 < x < 11
20: 2 < x < 8
21: Can't be a triangle, just a line
Step-by-step explanation:
Triangle inequality: the sum of two side measures must be greater than the third number:
A) 3, 4, 6: 3 + 4 > 6, 4 + 6 > 3, 6 + 3 > 4 - Is a triangle
B) 6, 9, 15: 6 + 9 = 15, 9 + 15 > 6, 6 + 15 > 9 - Not a triangle
C) 8, 8, 8: Equal length = equilateral triangle
D) 2, 4, 5: 2 + 4 > 5, 4 + 5 > 2, 5 + 2 > 4 - IS a triangle
E) 1.5, 2.5, 3: 1.5 + 2.5 > 3, 2.5 + 3 > 1.5, 1.5 + 3 > 2.5 - Is a triangle
A) 2, 5, 9: 2 + 5 < 9 - Not a triangle
B) 6, 6, 7: 6 + 6 > 7, 6 + 7 > 6 - IS a triangle
C) 6, 4, 2: 4 + 2 = 6, not a triangle
D) 7, 8, 1: 7 + 1 = 8, not a triangle
E) 5, 5, 5: Equilateral triangle
17) 11, 13: 11 + 13 = 24, 13 - 11 = 2 --> 2 < x < 24
18) 34, 35: 35 + 34 = 69, 35 - 34 = 1, so 1 < x < 69
19) 9, 2: 9 + 2 = 11, 9 - 2 = 7 --> 7 < x < 11
20) 3, 5: 3 + 5 = 8, 5 - 3 = 2 --> 2 < x < 8
21) 3, 0 - Can't be a triangle, just a line: One side can't have a value of 0.
