Answer:
[tex]8,5,10,13[/tex]
Step-by-step explanation:
Let
x-----> the length of the third side
we know that
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side
so
case A)
[tex]7+9 >x\\16> x\\x<16\ units[/tex]
case B)
[tex]7+x >9\\x>9-7\\ x>2\ units[/tex]
The solution for the length of the third side is the interval------> [tex](2,16)[/tex]
All real numbers greater than [tex]2[/tex] and less than [tex]16[/tex]
therefore
the solutions are
[tex]8,5,10,13[/tex]
