1. **State the problem:** We are given two similar quadrilaterals $WXYZ \sim FIHG$ and some side lengths. We need to find the lengths of segments $GH$ and $WX$. 2. **Identify corresponding sides:** Since $WXYZ \sim FIHG$, corresponding vertices match in order: $W \leftrightarrow F$, $X \leftrightarrow I$, $Y \leftrightarrow H$, $Z \leftrightarrow G$. 3. **Given side lengths:** - $XY = 4$ corresponds to $IH = 24$ - $WZ = 9$ corresponds to $FG = 60$ - $IF = 48$ corresponds to $WX$ (since $W \leftrightarrow F$ and $X \leftrightarrow I$) 4. **Find scale factor:** The ratio of corresponding sides is constant. Using $XY$ and $IH$: $$\text{scale factor} = \frac{IH}{XY} = \frac{24}{4} = 6$$ 5. **Find $WX$:** Since $WX$ corresponds to $FI$ (or $IF$), and $IF = 48$: $$\frac{FI}{WX} = 6 \implies WX = \frac{FI}{6} = \frac{48}{6} = 8$$ 6. **Find $GH$:** Since $GH$ corresponds to $YZ$ and $YZ$ corresponds to $HG$ (check order carefully). Given $WZ = 9$ corresponds to $FG = 60$, so: $$\frac{FG}{WZ} = 6 \implies \frac{60}{9} = 6.666...$$ which contradicts the previous scale factor. So we must verify the correct pairs. Actually, $Z \leftrightarrow G$ and $Y \leftrightarrow H$, so $YZ$ corresponds to $GH$. Since $XY = 4$ corresponds to $IH = 24$, scale factor is 6. Similarly, $WZ = 9$ corresponds to $FG = 60$, ratio $60/9 = 6.666...$ which is not equal to 6. This suggests a possible typo or that the scale factor is not consistent. But since the problem states similarity, we use the scale factor from $XY$ and $IH$. Therefore, to find $GH$ corresponding to $YZ$, we need $YZ$ length, but it is not given. However, $GH$ corresponds to $YZ$, so: $$GH = 6 \times YZ$$ But $YZ$ is unknown. Since $WZ = 9$ corresponds to $FG = 60$, ratio is $60/9 = 6.666...$, which is inconsistent. Assuming the scale factor is $6$, then: $$GH = 6 \times YZ$$ But $YZ$ is unknown, so we cannot find $GH$ directly. Alternatively, if $GH$ corresponds to $YZ$, and $GH$ is unknown, but $FG = 60$ corresponds to $WZ = 9$, then scale factor is $60/9 = 6.666...$. Since the problem asks for $GH$ and $WX$, and $WX$ corresponds to $FI = 48$, we found $WX = 8$. For $GH$, since $GH$ corresponds to $YZ$, and $YZ$ is unknown, we cannot find $GH$ without $YZ$. **Conclusion:** - $WX = 8$ - $GH$ cannot be determined with given data. **Final answers:** $$WX = 8$$ $$GH = \text{unknown}$$