1. The problem asks which proportion can be used to find the value of $x$ in similar triangles with sides 6 cm, 2.5 cm, 21 cm, and $x$. 2. For similar triangles, corresponding sides are proportional, so the ratio of one pair of sides equals the ratio of the other pair: $$\frac{6}{2.5} = \frac{21}{x}$$ 3. This means the correct proportion is $$\frac{6}{2.5} = \frac{21}{x}$$. 4. To find $x$, cross-multiply: $$6 \times x = 2.5 \times 21$$ $$6x = 52.5$$ 5. Divide both sides by 6: $$x = \frac{52.5}{6} = 8.75$$ 6. For the second problem, given smaller side 0.5 m and larger side 2 m, and corresponding sides 6 cm and 21 cm, find $x$. 7. Set up the proportion: $$\frac{0.5}{2} = \frac{6}{x}$$ 8. Cross-multiply: $$0.5 \times x = 2 \times 6$$ $$0.5x = 12$$ 9. Divide both sides by 0.5: $$x = \frac{12}{0.5} = 24$$ Final answers: - For the first problem, the correct proportion is $$\frac{6}{2.5} = \frac{21}{x}$$ and $x = 8.75$. - For the second problem, $x = 24$.