To solve for $j$, we need to analyze the diagram provided. It seems that triangles $\triangle ABC$ and $\triangle BDE$ are similar because they share proportional angles:

1. Angle $\angle ABC = \angle BDE$ (both are right angles).
2. Angle $\angle CAB = \angle EBD$ (matching marked angles).

From the similarity of the triangles, we can use the proportionality of corresponding sides. Specifically, we write:

$\frac{AB}{BE} = \frac{AC}{BD}$

Substituting the known values:

• $AB = 20 \, \text{m}$
• $BE = 36 \, \text{m}$
• $AC = 27 \, \text{m}$
• $BD = j$

Thus, the proportion becomes: $\frac{20}{36} = \frac{27}{j}$

Solving for $j$:

1. Cross-multiply: $20j = 36 \cdot 27$

2. Simplify: $20j = 972$

3. Solve for $j$: $j = \frac{972}{20} = 48.6$

Final Answer:

$j = 48.6 \, \text{m}$

Would you like further explanation or details? Here are some related questions for practice:

1. How do you determine whether two triangles are similar?
2. What are the properties of proportional sides in similar triangles?
3. How do you set up proportions based on similar triangles?
4. Can you solve for the missing side if a different side was unknown?
5. How do right angles influence triangle similarity?

Tip: When working with similar triangles, always confirm that the angles match before using side ratios!