Which set of segment lengths could be used to construct a triangle

Option D) 13, 2, 12

Step-by-step 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