To determine the length of side QS in triangle QRS that is similar to triangle ABC, we need to know the corresponding sides of both triangles.
Since the triangles are similar, the ratios of the lengths of the corresponding sides are equal. Let's denote the sides of triangle ABC as \( a \), \( b \), and \( c \) corresponding to sides \( QR \), \( QS \), and \( RS \) of triangle QRS respectively.
You can find side QS by using the following proportionality based on the similarity of the triangles:
\[ \frac{AB}{QR} = \frac{AC}{QS} = \frac{BC}{RS} \]
If you know the length of side QR in triangle QRS and the corresponding side AB in triangle ABC, along with the lengths of AC and BC, you can set up a proportion to find QS.
For an exact answer, please provide the specific side lengths of triangle ABC and one of the sides of triangle QRS.
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