I'm trying to find the length of the segment from $H$ to $J$. The problem states the length of the segment from $B$ to $E$ is $494$, along with a couple ratios of the sides. $BC:CD = 2:3$ and $DE:EF:FG = 2:3:4$. The problem also makes it clear that $B, C$ and $D$ are collinear ; $D, E, F$ and $G$ are collinear ; $C, H$ and $G$ are collinear ; $B, H, J$ and $E$ are collinear and $C, J$ and $F$ are collinear, as seen in the diagram.
Since they give the length of $BE$, I believe I am supposed to find the ratio between $BE$ and $HJ$. However, they don't give any angles, nor relate the two given ratios together, so I'm doubting that there are any similar triangles or angle bisectors that could be used.
I remember reading that Ceva's theorem can be used to relate the ratios of sides, but upon further research, there should be three cevians and a point which they meet for the theorem to be used. Could some of the lines be extended to achieve this effect? Or is this even the right approach to the problem?