Answer:
RS = 11
Step-by-step explanation:
well from the mid-point theorem we have that
[tex]\triangle PRS \sim \triangle PNQ[/tex]
by a ratio of
[tex]1:2[/tex]
so
[tex]\frac{RS}{NQ}=\frac{1}{2}\\\\2[\frac{RS}{NQ}]=2[\frac{1}{2}]\\\\\frac{2RS}{NQ}=1\\\\NQ[\frac{2RS}{NQ}]=NQ[1]\\\\2RS=NQ[/tex]
and now we plug in
[tex]RS = 5x-39\\\\NQ = 4x-18[/tex]
[tex]2[5x-39]=4x-18\\\\10x-78=4x-18\\\\10x-4x=-18+78\\\\6x=60\\\\x=10[/tex]
so the length of RS is
[tex]RS = 5x-39\\\\RS = 5(10)-39\\\\RS=50-39\\\\RS=11[/tex]
