1. **Problem Statement:** We have two triangles, △ABC and △A'B'C', where △A'B'C' is a scaled copy of △ABC. We know the sides of △ABC: AB = 5, BC = 2, AC = 6, and the sides of △A'B'C': A'B' = 14, B'C' = x (unknown), A'C' = 16.8. 2. **Understanding the problem:** Since △A'B'C' is a scaled copy of △ABC, the sides are proportional. This means the ratios of corresponding sides are equal. 3. **Set up the ratios:** - For AB and A'B': $$\frac{5}{14}$$ - For BC and B'C': $$\frac{2}{x}$$ - For AC and A'C': $$\frac{6}{16.8}$$ 4. **Complete the first equation:** The problem asks to complete the equation $$\frac{5}{14} = ___$$. Since the triangles are similar, this ratio equals the ratio of the other corresponding sides. So, $$\frac{5}{14} = \frac{2}{x}$$ 5. **Complete the second equation:** Similarly, the problem asks to complete $$\frac{5}{2} = ___$$. This is the ratio of AB to BC in triangle ABC, so the corresponding ratio in the scaled triangle is $$\frac{5}{2} = \frac{14}{x}$$ 6. **Solve for x using the first equation:** $$\frac{5}{14} = \frac{2}{x} \implies 5x = 14 \times 2 = 28 \implies x = \frac{28}{5} = 5.6$$ 7. **Verify with the second equation:** $$\frac{5}{2} = \frac{14}{x} \implies 5x = 2 \times 14 = 28 \implies x = \frac{28}{5} = 5.6$$ 8. **Check with the third ratio:** $$\frac{6}{16.8} = \frac{6}{16.8} = \frac{5}{14} = 0.3571$$ approximately, confirming the scale factor. **Final answer:** - $$\frac{5}{14} = \frac{2}{x}$$ - $$\frac{5}{2} = \frac{14}{x}$$ - $$x = 5.6$$