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The problem involves two similar triangles, and you are tasked with finding the unknown value of \( x \), which represents the height of the smaller triangle. The values given are:

- \( a = 2 \) (the base of the smaller triangle),
- \( b = 6 \) (the height of the larger triangle), and
- \( 5 \) as the base of the larger triangle.

Since the triangles are similar, the corresponding sides of the triangles are proportional. This gives us the following proportion:

\[
\frac{x}{b} = \frac{a}{5}
\]

Substitute the known values \( a = 2 \) and \( b = 6 \):

\[
\frac{x}{6} = \frac{2}{5}
\]

Now, solve for \( x \):

\[
x = \frac{2}{5} \times 6 = \frac{12}{5} = 2.4
\]

Thus, \( x = 2.4 \). The correct answer is 2.4 (rounded to the nearest tenth). It seems you initially entered 4.6, but the correct value is 2.4.

Let me know if you have any questions or need further clarification.

Here are some additional related questions:
1. How do you identify similar triangles in different geometric figures?
2. How do proportions work when dealing with similar shapes?
3. What are other applications of similar triangles in real-world problems?
4. How would the problem change if the base of the smaller triangle was unknown instead of the height?
5. Can this concept of similar triangles be extended to 3D figures like pyramids?

**Tip:** Always ensure the sides you're comparing in similar triangles are corresponding (matching) sides, based on their relative positions.

The figure shown below contains two similar triangles. Find the unknown measure indicated by a variable. Answer to the nearest tenth. (Assume a = 2 and b = 6.)

This problem involves finding the unknown height of a smaller triangle using the concept of similar triangles. With given dimensions (a = 2, b = 6, base = 5), students will apply proportions to solve for the height x. Suitable for Grades 8-10.

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