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This problem involves solving for \( x \) in two similar triangles. We can apply the concept of similar triangles to set up a proportion between corresponding sides. 

The triangles \( \triangle JML \) and \( \triangle JNK \) are similar, so we can use the corresponding side lengths to form a proportion.

From the diagram:
- \( JL \) corresponds to \( JK \).
- \( JM \) corresponds to \( JN \).
- \( ML \) corresponds to \( NK \).

The sides provided are:
- \( JM = 6.8 \), \( JN = 3.4 \)
- \( ML = x \), \( NK = 5.6 \)

We can set up the proportion:
\[
\frac{JM}{JN} = \frac{ML}{NK}
\]
Substitute the known values:
\[
\frac{6.8}{3.4} = \frac{x}{5.6}
\]
Simplify the left side:
\[
2 = \frac{x}{5.6}
\]
Now solve for \( x \):
\[
x = 2 \times 5.6 = 11.2
\]

The value of \( x \) should be \( 11.2 \). It seems the answer entered, \( 4.1 \), is incorrect based on the given information.

Would you like a further breakdown of any steps?

Here are five related questions for practice:
1. How do you identify similar triangles?
2. How can you verify if two triangles are similar?
3. What are some common properties of similar triangles?
4. Can you explain the concept of corresponding sides in similar triangles?
5. How do you solve a proportion like \( \frac{a}{b} = \frac{c}{d} \)?

**Tip:** Always simplify ratios before solving proportions. This reduces errors and speeds up the process!

Solve for x. Round your answer to the nearest tenth if necessary. The figure shows two similar triangles, \( \triangle JML \) and \( \triangle JNK \), with given side lengths.

Learn how to solve for the unknown side length x in a problem involving two similar triangles. This problem uses proportions between corresponding sides of similar triangles. Suitable for students in Grades 8-10.

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