1. **State the problem:** We have two similar quadrilaterals EFGH and IJKL. We know sides EH = 9.2 and EF = 11 in EFGH, and side LK = 43 in IJKL. We need to find the length of side IJ in IJKL. 2. **Recall similarity properties:** In similar polygons, corresponding sides are proportional. That means the ratio of any two corresponding sides in EFGH equals the ratio of their counterparts in IJKL. 3. **Identify corresponding sides:** Since EFGH ~ IJKL, the order of vertices corresponds. So: - E corresponds to I - F corresponds to J - G corresponds to K - H corresponds to L Therefore, side EF corresponds to IJ, and side EH corresponds to IL. 4. **Use the given sides:** We know EF = 11, EH = 9.2, and LK = 43. Since G corresponds to K and H corresponds to L, side GH corresponds to KL, but we don't have GH. However, we have LK = 43, which corresponds to GH. 5. **Find the scale factor:** The ratio of corresponding sides between IJKL and EFGH is the same. Using side EH and side IL (which corresponds to EH), but we don't have IL. Instead, we can use LK and GH if GH was known, but it's not. 6. **Assuming LK corresponds to GH, and since we don't have GH, we use EF and IJ:** We want to find IJ, which corresponds to EF. 7. **Find scale factor using LK and EH:** $$\text{Scale factor} = \frac{LK}{EH} = \frac{43}{9.2} \approx 4.6739$$ 8. **Calculate IJ:** $$IJ = EF \times \text{Scale factor} = 11 \times 4.6739 = 51.413$$ 9. **Round to nearest tenth:** $$IJ \approx 51.4$$ **Final answer:** The length of side IJ is approximately 51.4 units.