1. **State the problem:** We are given a triangle with vertices F, D, and E. Points G and H lie on sides FD and FE respectively, with segment GH parallel to base DE. Given lengths HE = 13.3, FG = 13.3, and FH = 16.7, we need to find the length of GD. 2. **Identify the key property:** Since GH is parallel to DE, triangle FGH is similar to triangle FDE by the AA similarity criterion. 3. **Set up the similarity ratios:** Corresponding sides of similar triangles are proportional: $$\frac{FG}{FD} = \frac{FH}{FE} = \frac{GH}{DE}$$ 4. **Express known lengths:** We know FG = 13.3, FH = 16.7, and HE = 13.3. Since H lies on FE, and HE = 13.3, then FE = FH + HE = 16.7 + 13.3 = 30. 5. **Find FD:** Since G lies on FD and FG = 13.3, let GD = x. Then: $$FD = FG + GD = 13.3 + x$$ 6. **Use the similarity ratio:** From similarity, $$\frac{FG}{FD} = \frac{FH}{FE}$$ Substitute known values: $$\frac{13.3}{13.3 + x} = \frac{16.7}{30}$$ 7. **Solve for x:** Cross-multiply: $$13.3 \times 30 = 16.7 \times (13.3 + x)$$ $$399 = 16.7 \times 13.3 + 16.7x$$ Calculate: $$16.7 \times 13.3 = 222.11$$ So: $$399 = 222.11 + 16.7x$$ Subtract 222.11: $$399 - 222.11 = 16.7x$$ $$176.89 = 16.7x$$ Divide both sides by 16.7: $$x = \frac{176.89}{16.7}$$ Intermediate step with cancellation: $$x = \frac{\cancel{176.89}}{\cancel{16.7}}$$ Calculate: $$x \approx 10.6$$ 8. **Final answer:** The length of GD is approximately **10.6** units.