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The problem shows two right triangles with the goal of finding the length of \( x \). The key observation is that these triangles are similar, meaning their corresponding sides are proportional.

The larger triangle has sides of 24 (base), 18 (height), and a hypotenuse of unknown length. The smaller triangle inside has sides \( x \), 12, and the same angle.

We can use the property of similar triangles to set up the following proportion:

\[
\frac{x}{24} = \frac{12}{18}
\]

Now, let's solve for \( x \).The value of \( x \) is \( 16 \).

Would you like more details on this process or have any other questions?

Here are 5 related questions you might find helpful:
1. How do you prove that the triangles are similar?
2. What are other methods to solve similar triangles?
3. How do we calculate the hypotenuse in right triangles?
4. How does the Pythagorean theorem apply to this problem?
5. What are the rules for proportionality in triangles?

**Tip:** When dealing with similar triangles, always identify corresponding sides and set up a proportion based on these.

Find the length of x in the given pair of similar triangles with side lengths 24, 18, 12, and x.

Learn how to find the length of x using the concept of similar triangles. This problem demonstrates how to set up proportions based on corresponding sides in similar right triangles, suitable for students in Grades 8-10.

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