https://file.aiquickdraw.com/mathbot/file/1729530364514vg8eys2g.jpg

In the image, we have a right triangle where we need to find the value of \( x \). It looks like the larger triangle has legs of 10 and 25, and inside it, there is a smaller right triangle with legs of 4 and \( x \). The two triangles are similar because they share the same angles.

### Using similarity of triangles:
- Since the triangles are similar, the corresponding sides of the triangles are proportional.

Let’s set up the proportion using the corresponding sides:

\[
\frac{x}{25} = \frac{4}{10}
\]

Now, solve for \( x \):

\[
x = \frac{4}{10} \times 25
\]

\[
x = \frac{100}{10} = 10
\]

So, the value of \( x \) is \( 10 \).

Would you like a detailed explanation of any step? Here are five related questions:

1. How do we determine when two triangles are similar?
2. What are the properties of similar triangles?
3. How can proportions be used to solve for unknowns in triangles?
4. What is the Pythagorean Theorem, and can it be used here?
5. Are there other methods to verify the value of \( x \)?

**Tip**: Always look for shared angles and sides when trying to identify similar triangles, as it simplifies solving geometric problems.

Find the value of x in the given triangle where one smaller triangle is inscribed within a larger triangle with sides proportional to 4, x, and 25, and 10.

Learn how to solve for x using the similarity of triangles in this right triangle problem. The solution involves setting up proportions between the corresponding sides of two triangles. Suitable for students in Grades 8-10.

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