Question 944040
UNDERSTANDING the triangle inequality theorem is necessary.  Use it to formulate the inequalities.


Let the "third" side length be x.
The first two lengths of the triangle sides are 18 and 3+2x.  Those are directly from the description.


Now, form the inequality statements using the theorem:
{{{system(18+2x+3>x,18+x>2x+3,2x+3+x>18)}}}


Simplify the system:

{{{system(21>-x,15>x,3x>15)}}}


The first simplified inequality does not help any.
The next two are these:
{{{system(x<15,x>5)}}}, when simplified.


Solution in more condensed form, {{{highlight(5<x<15)}}} for the third side.