Answer:
Triangle Inequality Theorem
see the explanation
Step-by-step explanation:
see the attached figure to better understand the 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
In the triangle ABC of the figure
Applying the Triangle Inequality Theorem
1) First case
[tex]10+8 > x[/tex]
solve for x
Combine like terms left side
[tex]18 > x[/tex]
Rewrite
[tex]x < 18\ units[/tex]
2) Second case
[tex]8+x > 10[/tex]
solve for x
subtract 8 both sides
[tex]x > 10-8[/tex]
[tex]x > 2\ units[/tex]
therefore
The range of possible lengths of the third side AB is the interval (2,18)
All real numbers greater than 2 units and less than 18 units
