Answer:
[tex]QS=68\ units[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
r is the midpoint of qs
so
QR=RS
QS=QR+RS------> QS=2RS -----> equation A
RT=RS+ST ----> equation B
see the attached figure to better understand the problem
Substitute the given values in the equation B and solve for x
[tex]8x-43=(2x-4)+(4x-1)[/tex]
[tex]8x-43=6x-5[/tex]
[tex]8x-6x=43-5[/tex]
[tex]2x=38[/tex]
[tex]x=19[/tex]
step 2
Find the value of RS
[tex]RS=2x-4[/tex]
substitute the value of x
[tex]RS=2(19)-4[/tex]
[tex]RS=34\ units[/tex]
step 3
Find the value of QS
Remember equation A
QS=2RS
so
[tex]QS=2(34)=68\ units[/tex]
