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The problem shows two triangles, \( \triangle ABC \) and \( \triangle XYZ \), which are similar. In similar triangles, the corresponding sides are proportional. We are asked to find the unknown side of \( \triangle ABC \).

Given dataThe problem shows two triangles, \( \triangle ABC \) and \( \triangle XYZ \), which are similar. In similar triangles, the corresponding sides are proportional. We are asked to find the unknown side of \( \triangle ABC \).

Given 

- \( AB = 2 \), \( BC = 4 \), and \( AC = ? \) for \( \triangle ABC \).
- \( XY = 18 \), \( YZ = 36 \), and \( XZ = 27 \) for \( \triangle XYZ \).

To solve for the unknown side \( AC \), we use the property of similar triangles, which gives us the following proportion for corresponding sides:

\[
\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}
\]

### Step-by-Step Solution:

1. Set up the proportion for corresponding sides:
\[
\frac{AB}{XY} = \frac{AC}{XZ}
\]
\[
\frac{2}{18} = \frac{AC}{27}
\]

2. Solve for \( AC \):
\[
\frac{2}{18} = \frac{AC}{27}
\]
Cross-multiply to solve:
\[
2 \times 27 = 18 \times AC
\]
\[
54 = 18 \times AC
\]
\[
AC = \frac{54}{18} = 3
\]

Thus, the unknown side \( AC \) is \( 3 \).

Would you like more details on the solution or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the property of similar triangles regarding corresponding angles?
2. How can you check if two triangles are similar by using their angles?
3. Can the ratio of perimeters of similar triangles be used to find unknown sides?
4. How do you apply proportions in other geometric figures, such as quadrilaterals?
5. What are some practical applications of similar triangles in real-world problems?

**Tip:** In similar triangles, all corresponding angles are equal, and all corresponding sides are proportional. This concept is crucial in solving various geometry problems.

△ABC and △XYZ are similar triangles. Find the unknown side length of △ABC.

Learn how to find the unknown side AC in △ABC, where △ABC is similar to △XYZ. By applying the property of similar triangles and solving using proportions, the unknown side is found to be 3.

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