The question is about finding the length $x$ in two similar triangles, $\triangle ABC \sim \triangle XYZ$.

Since the triangles are similar, their corresponding sides are proportional:

$\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}$

Given:

• $AB = 50$, $BC = 40$ in $\triangle ABC$
• $YZ = 20$, and we need to find $XY = x$.

Using the proportion $\frac{AB}{XY} = \frac{BC}{YZ}$:

$\frac{50}{x} = \frac{40}{20}$

Simplify $\frac{40}{20}$ to get $2$:

$\frac{50}{x} = 2$

Now, solve for $x$ by cross-multiplying:

$50 = 2x$ $x = \frac{50}{2} = 25$

Thus, the appropriate value for $x$ is 25.

Let me know if you want more details or have any questions.

Related Questions:

1. What does it mean for triangles to be similar?
2. How are proportions used in similar triangles?
3. What are corresponding sides and angles in similar triangles?
4. How can you verify if two triangles are similar?
5. What other properties are preserved in similar triangles?

Tip: When working with similar triangles, always ensure that you match corresponding sides correctly to set up proportions accurately.