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Given that the polygons \( QRSTU \) and \( FEDHG \) are similar, we can set up a proportion to find the lengths of segments \( EF \) and \( RS \).

Since similar polygons have proportional side lengths, we’ll find the scale factor by comparing corresponding sides. Here, we have:
1. \( QS = 6 \)
2. \( HD = 27 \)

The scale factor from \( QRSTU \) to \( FEDHG \) is:
\[
\frac{HD}{QS} = \frac{27}{6} = 4.5
\]

### Finding \( EF \)
To find \( EF \), we use the corresponding side \( TU = 4 \) from \( QRSTU \):
\[
EF = TU \times 4.5 = 4 \times 4.5 = 18
\]

### Finding \( RS \)
To find \( RS \), we use the corresponding side \( FG = 6 \) from \( FEDHG \):
\[
RS = FG / 4.5 = 6 / 4.5

Learn how to find side lengths EF and RS in the similar polygons QRSTU and FEDHG using proportions. This problem covers polygon similarity and proportional side lengths, suitable for students in Grades 8-10.

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