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To solve for \( y \) in this similar triangle problem, we need to understand the relationship between the triangles. Since \(\triangle ABC \sim \triangle XYZ\), we know that the corresponding sides are proportional.

The corresponding sides are:
- \( AB \) corresponds to \( XY \),
- \( BC \) corresponds to \( XZ \),
- \( AC \) corresponds to \( YZ \).

Given values:
- \( AB = 34 \), \( AC = 16 \), and \( BC = 30 \) for \(\triangle ABC\),
- \( XY = 15 \) and \( XZ = x \) for \(\triangle XYZ\).

We can set up a proportion using the corresponding sides:

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

To find \( YZ \) (which corresponds to \( AC \)), we use the proportion with \( AC \) and \( XY \):

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

Substitute the known values:

\[
\frac{34}{15} = \frac{16}{YZ}
\]

Cross-multiply to solve for \( YZ \):

\[
34 \cdot YZ = 16 \cdot 15
\]
\[
34 \cdot YZ = 240
\]
\[
YZ = \frac{240}{34} = 7.0588
\]

If you meant the hypotenuse length in

How to find the value of y in the similar triangles ΔABC and ΔXYZ?

Learn how to find the missing side length in similar triangles ΔABC and ΔXYZ by setting up and solving proportions. This problem involves understanding triangle similarity, setting up ratios between corresponding sides, and solving for unknown lengths. Suitable for students in Grades 8-10.

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