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If the given triangles are similar, what is the value of *x* in the triangle *ABC*?

To find the value of \(x\) in triangle \(ABC\), we need to use the concept of similar triangles. When two triangles are similar, their corresponding sides are proportional.

In the image provided:

- Triangles \(DEF\) and \(ABC\) are similar.
- \(DE\) corresponds to \(AB\), \(DF\) corresponds to \(AC\), and \(EF\) corresponds to \(BC\).

Given:
- \(DE = 12\) cm, \(EF = 16\) cm.
- \(AB = x\) cm, \(BC = 32\) cm.

Using the similarity property, we can write the proportion:
\[
\frac{DE}{AB} = \frac{EF}{BC}
\]

Substitute the given values:
\[
\frac{12}{x} = \frac{16}{32}
\]

Let's solve this proportion for \(x\).The value of \(x\) in triangle \(ABC\) is \(24\) cm.

Would you like a detailed explanation of how the solution was derived, or do you have any other questions? Here are five related questions to explore further:

1. How can we determine if two triangles are similar?
2. What are the properties of similar triangles?
3. How can the Pythagorean theorem be applied to these triangles?
4. If a third triangle is added and is also similar, how do we find its missing sides?
5. What are some real-life applications of similar triangles?

**Tip:** When working with similar triangles, remember that their corresponding angles are equal and their corresponding sides are in proportion.

If the given triangles are similar, what is the value of x in the triangle ABC?

Learn how to find the missing side 'x' in triangle ABC using the concept of similar triangles and proportionality. This problem involves applying the similarity theorem and is suitable for students in Grades 7-9.

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