Answer:
All real numbers greater than [tex]10\ cm[/tex] and less than [tex]50\ cm[/tex]
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
c-----> the length of the third side
Applying the theorem
case A)
[tex]20+30> c\\50> c\\ c< 50\ cm[/tex]
case B)
[tex]20+c > 30\\c > 30-20\\c> 10\ cm[/tex]
The solution for the measure of the third side of the triangle is the interval
[tex](10,50)[/tex]
All real numbers greater than [tex]10\ cm[/tex] and less than [tex]50\ cm[/tex]
