Question

Triangle EFG is similar to triangle HIJ. Find the measure of side HI. Figures are not drawn to scale.
E
F
G
H
I
J
3
2
8.4

Answer 1

I’ll assume the vertex order shows E↔H, F↔I, G↔J (so EF ↔ HI and FG ↔ IJ). If FG = 2 and the corresponding side IJ = 8.4, the scale factor from triangle EFG to HIJ is 8.4/2 = 4.2. Thus

HI = EF × 4.2 = 3 × 4.2 = 12.6.

If the given numbers refer to different sides, tell me which length corresponds to which side and I’ll recompute.