We have two similar triangles:

• Triangle JEN
• Triangle JGH

Since NE is parallel to GH, the two triangles are homothetic (similar), meaning we can use the proportionality of corresponding sides.

Given values:

• JE = 40, NE = 29.5
• JG = 56, JH = 60.2
• GH = 41.3

We want to find JN.

Since NE // GH, the ratio between the similar triangles is:

$\frac{JN}{JH} = \frac{NE}{GH}$

Substituting the known values:

$\frac{JN}{60.2} = \frac{29.5}{41.3}$

$JN = 60.2 \times \frac{29.5}{41.3}$

$JN \approx 60.2 \times 0.7144$

$JN \approx 43.0$

Thus, the length of JN is approximately 43.0.

Would you like a step-by-step breakdown or additional explanations?

Related Questions:

1. How do we determine that the triangles are similar?
2. What other properties remain unchanged in similar triangles?
3. Can this problem be solved using another method?
4. What if the given values were different—how would we adjust our approach?
5. How does the parallel condition help in solving the problem?

Tip:

When working with similar triangles, always check for parallel lines, corresponding angles, and proportional sides!