Answer:
[tex]RS=25\ units[/tex]
Step-by-step explanation:
we know that
If line I s a perpendicular bisector of line segment R Q at point T
then
T is the midpoint of line segment RQ
and
[tex]RT=TQ[/tex]
we have
[tex]TQ=18\ units[/tex]
so
[tex]RT=18\ units[/tex]
Find the value of x
we have
[tex]RT=2x+10[/tex]
substitute the value of RT
[tex]18=2x+10[/tex]
solve for x
[tex]2x=18-10\\2x=8\\x=4[/tex]
Find the value of SQ
[tex]SQ=9x-11[/tex]
substitute the value of x
[tex]SQ=9(4)-11=25\ units[/tex]
we have that
Triangle RTS and Triangle QTS are congruent by SAS
see the attached figure to better understand the problem
so
[tex]RS=SQ[/tex]
therefore
[tex]RS=25\ units[/tex]
