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The image shows two similar right triangles. The smaller triangle has legs of lengths 3 and 6, while the larger triangle has a leg of 8 and an unknown hypotenuse \( x \). Since the triangles are similar, their corresponding sides are proportional.

We can set up a proportion using the corresponding sides:

\[
\frac{3}{6} = \frac{8}{x}
\]

To solve for \( x \), cross-multiply:

\[
3x = 6 \times 8
\]

\[
3x = 48
\]

Now, divide both sides by 3:

\[
x = \frac{48}{3} = 16
\]

So, the length of \( x \) is 16.

Do you need further details or have any questions? 

Here are 5 related questions:
1. How do you prove two triangles are similar?
2. What is the relationship between the angles of similar triangles?
3. How can you use the Pythagorean theorem to solve for sides in a right triangle?
4. What are some real-world applications of similar triangles?
5. How does the ratio of side lengths in similar triangles affect their areas?

**Tip**: Always double-check the similarity condition before applying proportions.

Learn how to find the length x in a set of similar right triangles using the concept of proportions. This problem explains the key steps of setting up a proportion based on corresponding sides and solving for the unknown using cross-multiplication. Suitable for students in Grades 8-10.

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