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
so
Let
s------> the length of the third side
[tex]25+s > 35 \\ s > 35-25 \\ s> 10\ cm[/tex]
[tex]25+35 > s \\ 60 > s \\ s< 60\ cm[/tex]
[tex]10\ cm < s < 60\ cm[/tex]
therefore
The answer part a) is
[tex]10\ cm < s < 60\ cm[/tex]
we know that
the perimeter of a triangle is the sum of the length sides
In this problem
[tex]P=25+35+s\\P=60+s[/tex]
For [tex]s> 10\ cm[/tex]
the perimeter is equal to
[tex]P > 60+10\\ P>70\ cm[/tex]
For [tex]s< 60\ cm[/tex]
the perimeter is equal to
[tex]P < 60+60\\ P<120\ cm[/tex]
so
[tex]70\ cm < P < 120\ cm[/tex]
therefore
the answer part b) is
[tex]70\ cm < P < 120\ cm[/tex]
