ANSWER
NK = 59.11
EXPLANATION
If two figures are similar, then the ratio between corresponding sides must be constant. For these two figures, this means,
[tex]\frac{NK}{GJ}=\frac{LM}{HI}=\frac{NM}{JI}=\frac{GH}{KL}[/tex]
We know that GJ = 14, LM = 38 and HI = 9,
[tex]\frac{NK}{14}=\frac{38}{9}[/tex]
Multiply both sides by 14,
[tex]NK=14\cdot\frac{38}{9}\approx59.11[/tex]
Rounded to the nearest hundredth, the measure of side NK is 59.11.
