1. **State the problem:** We are given two similar triangles, BCD and EFG. We know sides BC = 1.8, BD = 2 in triangle BCD, and side EG = 10 in triangle EFG. We need to find the length of side FG. 2. **Recall the property of similar triangles:** Corresponding sides of similar triangles are proportional. This means: $$\frac{BC}{EF} = \frac{BD}{EG} = \frac{CD}{FG}$$ 3. **Identify corresponding sides:** Since triangles BCD and EFG are similar, side BC corresponds to EF, BD corresponds to EG, and CD corresponds to FG. 4. **Set up the proportion to find FG:** We know BD = 2 and EG = 10, so the scale factor from triangle BCD to EFG is: $$\frac{EG}{BD} = \frac{10}{2} = 5$$ 5. **Use the scale factor to find FG:** Since FG corresponds to CD, and the scale factor is 5, we need the length of CD in triangle BCD to find FG. 6. **Find CD in triangle BCD:** Using the Pythagorean theorem in triangle BCD (assuming right triangle or given data), if not given, we cannot find CD directly. However, since BC = 1.8 and BD = 2, and if BD is the hypotenuse, then: $$CD = \sqrt{BD^2 - BC^2} = \sqrt{2^2 - 1.8^2} = \sqrt{4 - 3.24} = \sqrt{0.76} \approx 0.8718$$ 7. **Calculate FG:** Multiply CD by the scale factor 5: $$FG = 5 \times 0.8718 = 4.359$$ 8. **Final answer:** The length of side FG is approximately 4.36 units.