We have a segment RT, and S is a point between R and T.
The length of RT is 4x-4.
The length of RS is 2x+6.
The length of ST is 16.
As S is between R and T, we can write:
[tex]RS+ST=RT[/tex]Then:
[tex]\begin{gathered} RS+ST=RT \\ 2x+6+16=4x-4 \\ 22+4=4x-2x \\ 26=2x \\ x=\frac{26}{2} \\ x=13 \end{gathered}[/tex]With the value of x, we can calculte RS:
[tex]RS=2x+6=2(13)+6=26+6=32[/tex]The length of RS is 32.
