https://file.aiquickdraw.com/mathbot/file/17406138953580oncj7l7.jpg

The problem presents two similar triangles, where the smaller triangle is similar to the larger one. You are tasked with finding the value of \( x \) by setting up a proportion.

Given the diagram in the image, we have:
- The smaller triangle has a side length of 8.
- The larger triangle has a side length of 10.
- The corresponding side length in the smaller triangle is \( x \), and the corresponding side in the larger triangle is 8.

To solve for \( x \), we can use the property of similar triangles, which states that corresponding sides are proportional. Therefore, the proportion can be set up as follows:

\[
\frac{x}{8} = \frac{8}{10}
\]

Now, solve for \( x \):

1. Cross-multiply:
   \[
   x \cdot 10 = 8 \cdot 8
   \]

2. Simplify:
   \[
   10x = 64
   \]

3. Divide both sides by 10:
   \[
   x = \frac{64}{10} = 6.4
   \]

Thus, \( x = 6.4 \).

Would you like further details or explanations on this? Let me know if you need any more steps or a deeper understanding!

Here are 5 related questions for further practice:
1. How would you solve a similar triangle problem with more than one unknown side?
2. What is the scale factor between the two triangles in this problem?
3. How can you use similar triangles to find missing angles in a diagram?
4. How can you apply proportional reasoning to solve real-world problems involving similar triangles?
5. How do you verify if two triangles are indeed similar?

Tip: Always remember to check that the corresponding angles of similar triangles are equal before setting up a proportion.

Examine the diagram at right. The smaller triangle is similar to the larger triangle. Write a proportion and solve for x.

Learn how to solve for x using proportions in similar triangles. This problem involves applying the Basic Proportionality Theorem to find the unknown side of a smaller triangle when given the sides of two similar triangles. Suitable for students in Grades 7-9.

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