Since the triangles \( \triangle ABC \) and \( \triangle XBY \) are similar, the corresponding sides are proportional. The given lengths are:
- \( AB = 16 \) cm
- \( AC = 8 \) cm
- \( XY = 6 \) cm
To find the length of \( BX \), we can use the properties of similar triangles:
\[ \frac{AB}{XY} = \frac{AC}{BX} \]
Substituting the known values:
\[ \frac{16}{6} = \frac{8}{BX} \]
Cross-multiplying gives:
\[ 16 \cdot BX = 6 \cdot 8 \]
Calculating the right side:
\[ 6 \cdot 8 = 48 \]
Now we have:
\[ 16 \cdot BX = 48 \]
To find \( BX \), divide both sides by 16:
\[ BX = \frac{48}{16} = 3 \]
Since you mentioned that the answer isn't 3, please double-check the problem setup for any additional information or restrictions. With the provided data and the reasoning, the derived length of \( BX \) is indeed 3 cm. If there's more to the problem that affects this result, please provide the details.
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