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In the problem, the two triangles \( \triangle ABC \) and \( \triangle DEF \) are given as similar. This means that corresponding sides of the triangles are proportional. We are tasked with finding the missing side length \( AB \) (denoted as \( ? \)).

### Step-by-Step Solution:

1. Identify the sides of the similar triangles that correspond to each other:
   - \( AB \) corresponds to \( DE \)
   - \( BC \) corresponds to \( EF \)
   - \( AC \) corresponds to \( DF \)

2. The given side lengths are:
   - \( BC = 36 \), \( EF = 6 \)
   - \( AC = 30 \), \( DF = 5 \)
   - \( DE = 2 \)

3. Use the proportionality of corresponding sides:
   \[
   \frac{AB}{DE} = \frac{BC}{EF}
   \]
   Substituting the known values:
   \[
   \frac{AB}{2} = \frac{36}{6}
   \]
   Simplifying the right-hand side:
   \[
   \frac{AB}{2} = 6
   \]

4. Solve for \( AB \):
   \[
   AB = 6 \times 2 = 12
   \]

### Final Answer:
The missing side length \( AB \) is 12 units.

Would you like more details or have any other questions?

Here are five related questions to practice:
1. If \( \triangle ABC \) and \( \triangle DEF \) have angles of the same measure, what kind of triangles are these?
2. How do you determine if two triangles are similar based on their angles?
3. What happens to the area ratio of two similar triangles?
4. If \( DE = 3 \) and \( EF = 9 \), how would the missing side length \( AB \) change?
5. Can similar triangles ever have different angle measures? Why or why not?

**Tip:** In similar triangles, the ratio of corresponding sides is constant, making it easy to solve for unknown side lengths.

ΔABC and ΔDEF are similar. Find the missing side length of AB given BC = 36, AC = 30, DE = 2, DF = 5, and EF = 6.

Solve a problem involving two similar triangles, ΔABC and ΔDEF. Using the proportionality of corresponding sides, we calculate the missing side length AB when BC = 36, AC = 30, DE = 2, DF = 5, and EF = 6. Suitable for students in Grades 7-9.

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