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