Answer:
The range of possible values for third side is:
[tex]44>x>6[/tex]
Step-by-step explanation:
Given side lengths are:
19 and 25
Let x be the third side
Then according to the triangle in equality theorem that sum of two sides has to be greater than third side,
The inequalities will be:
[tex]19+25>x\\25+x>19\\19+x>25[/tex]
We have to solve these inequalities to find the range
So,
[tex]19+25> x => 44>x\\25+x>19 => x >19-25 => x>-6\\19+x>25 => x> 25-19 => x>6[/tex]
We have to exclude the solution with negative value because the length of a triangle cannot be negative so from the other two inequalities x has to be less than 44 and greater than 6
Hence,
The range of possible values for third side is:
[tex]44>x>6[/tex]
