1. **State the problem:** We have two similar polygons WXYZ and FIHG. We know some side lengths and need to find $GH$ and $WX$. 2. **Identify known sides:** - Polygon WXYZ: $YX=4$, $ZY=9$, $WX$ unknown. - Polygon FIHG: $FI=48$, $IH=24$, $HG=60$. 3. **Use similarity ratios:** Since polygons are similar, corresponding sides are proportional. 4. **Match corresponding sides:** - $W \leftrightarrow F$ - $X \leftrightarrow I$ - $Y \leftrightarrow H$ - $Z \leftrightarrow G$ 5. **Set up ratios:** $$\frac{YX}{IH} = \frac{4}{24} = \frac{1}{6}$$ 6. **Find $GH$ corresponding to $ZY$:** $$\frac{ZY}{GH} = \frac{9}{GH} = \frac{1}{6} \implies GH = 9 \times 6 = 54$$ 7. **Find $WX$ corresponding to $FI$:** $$\frac{WX}{FI} = \frac{WX}{48} = \frac{1}{6} \implies WX = \frac{48}{6} = 8$$ **Final answers:** $$GH = 54$$ $$WX = 8$$