Answer:
Option D) 13, 2, 12
Explanation:
The complete question is
Which set of segment lengths could be used to construct a triangle?
A) 2, 12, 19 B) 4, 7, 13 C) 4, 5, 12 D) 13, 2, 12
Note: If this problem does not coincide with the one requested by the student, the methodology used will be useful to solve any other similar problem.
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 2, 12, 19
Applying the Triangle Inequality Theorem
1) 2+2 > 19 ----> is not true
therefore
This set of segment lengths could not be used to construct a triangle
case B) we have 4, 7, 13
Applying the Triangle Inequality Theorem
1) 4+7 > 13 ----> is not true
therefore
This set of segment lengths could not be used to construct a triangle
case C) we have 4, 5, 12
Applying the Triangle Inequality Theorem
1) 4+5 > 12 ----> is not true
therefore
This set of segment lengths could not be used to construct a triangle
case D) we have 13, 2, 12
Applying the Triangle Inequality Theorem
1) 13+2 > 12 ----> is true
2) 13+12 > 2 ----> is true
3) 2+12 > 13 ---> is true
therefore
This set of segment lengths could be used to build a triangle