To determine the length of side \( QS \) in triangle \( QRS \), we need to use the property of similar triangles, which states that the ratios of the lengths of corresponding sides are equal.
Let's denote the lengths of the sides of triangle \( ABC \) as follows:
- \( AB \) corresponding to \( QR \)
- \( BC \) corresponding to \( RS \)
- \( AC \) corresponding to \( QS \)
We need the actual lengths of the sides from triangle \( ABC \) to establish the scale factor between the two triangles. If we had the lengths of the sides of triangle \( ABC \) and the length of one side of triangle \( QRS \), we could set up a proportion to find \( QS \).
For example, if the sides of triangle \( ABC \) were \( AB = a \), \( BC = b \), and \( AC = c \), and the corresponding side in triangle \( QRS \) were \( QR \) with a known length, say \( QR = k \), you could set up the ratios:
\[ \frac{AB}{QR} = \frac{AC}{QS} \]
From this proportion, you could solve for \( QS \):
\[ QS = \frac{AC \cdot QR}{AB} \]
If you provide the specific lengths of the sides of triangle \( ABC \) and the corresponding side from triangle \( QRS \), I can help you calculate the length of \( QS \).
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