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To find the value of the missing side \( x \) in the similar triangles, we can use the property that the ratios of corresponding sides of similar triangles are equal.

Given triangles:

- Larger triangle sides: 12, 20
- Smaller triangle sides: 3, \( x \)

The ratio of the corresponding sides should be equal. Therefore, we can set up the following proportion:

\[
\frac{12}{3} = \frac{20}{x}
\]

Now, solve for \( x \):

1. Simplify the ratio on the left side:

\[
\frac{12}{3} = 4
\]

2. Set up the equation:

\[
4 = \frac{20}{x}
\]

3. Cross-multiply to solve for \( x \):

\[
4x = 20
\]

4. Divide both sides by 4:

\[
x = \frac{20}{4} = 5
\]

So, the value of the missing side \( x \) is \( 5 \).

Would you like any more details or have any questions?

Here are 5 related questions that expand on this information:
1. What are the properties of similar triangles?
2. How can you verify that two triangles are similar?
3. How do you find the scale factor between two similar triangles?
4. Can the method used here apply to other geometric shapes? If so, how?
5. How does changing the lengths of sides in one triangle affect the other in similar figures?

**Tip:** When working with proportions, always ensure the ratios are set up with corresponding sides from each figure or shape.

This pair of figures is similar. Find the value of the missing side (x).

Learn how to find the missing side in similar triangles using proportions. This example shows how to apply the concept of proportional corresponding sides, perfect for students in grades 6-8 seeking to understand geometry fundamentals.

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