Answer:
Option d. 4, 8, 10
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Verify each case
case a) we have
15, 9, 3
Applying the triangle Inequality Theorem
1) 15+9 > 3
24> 3 ------> is true
2) 15+3 > 9
18 > 9 ----> is true
3) 9+3 > 15
12 > 15 ----> is not true
therefore
The set of lengths cannot be used to form the sides of a triangle
case b) we have
6,12,19
Applying the triangle Inequality Theorem
1) 6+12 > 19
18> 19 ------> is not true
therefore
The set of lengths cannot be used to form the sides of a triangle
case c) we have
11,6,3
Applying the triangle Inequality Theorem
1) 11+6 > 3
17> 3 ------> is true
2) 11+3 > 6
14 > 6 ----> is true
3) 6+3 > 11
9 > 11 ----> is not true
therefore
The set of lengths cannot be used to form the sides of a triangle
case d) we have
4,8,10
Applying the triangle Inequality Theorem
1) 4+8 > 10
12> 10 ------> is true
2) 4+10 > 8
14 > 8 ----> is true
3) 8+10 > 4
18 > 4 ----> is true
therefore
The set of lengths can be used to form the sides of a triangle
