https://file.aiquickdraw.com/mathbot/file/17272891624139vno3emu.jpg

The two triangles in the image are labeled as similar. When two triangles are similar, corresponding sides are proportional. From the figure, we can set up a proportion using the corresponding sides of the triangles.

The smaller triangle has sides 9 (corresponding to 19.8 in the larger triangle), 6 (corresponding to \(x\) in the larger triangle), and 5 (corresponding to 11 in the larger triangle).

We can set up the proportion based on the corresponding sides:
\[
\frac{6}{x} = \frac{9}{19.8}
\]

Now, solve for \(x\):

First, cross-multiply:
\[
6 \times 19.8 = 9 \times x
\]
\[
118.8 = 9x
\]

Divide both sides by 9 to solve for \(x\):
\[
x = \frac{118.8}{9} = 13.2
\]

So, the value of \(x\) is 13.2.

Would you like further details or have any questions?

Here are 5 related questions you might want to explore:
1. How do you prove that two triangles are similar?
2. Can the same approach be used to find other unknown sides in a pair of similar triangles?
3. What is the relationship between corresponding angles in similar triangles?
4. How can this proportionality be applied in real-life geometric problems?
5. What are some key differences between similar triangles and congruent triangles?

**Tip**: When working with similar triangles, always make sure the corresponding sides and angles are clearly identified to set up correct proportions.

In the figure, the two triangles are similar. What is the value of x?

Learn how to find the value of x using the concept of similar triangles and proportions. This problem involves key geometry concepts such as the AA similarity theorem and setting up proportions. Suitable for students in Grades 8-10.

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