1. **State the problem:** We need to find which ratios are equivalent to $4:9$. 2. **Recall the rule for equivalent ratios:** Two ratios $a:b$ and $c:d$ are equivalent if $\frac{a}{b} = \frac{c}{d}$. 3. **Check each ratio:** - For $7:21$, calculate $\frac{7}{21} = \frac{1}{3}$. - For $25:36$, calculate $\frac{25}{36}$ (cannot simplify further). - For $5:6$, calculate $\frac{5}{6}$ (cannot simplify further). - For $36:81$, calculate $\frac{36}{81} = \frac{4}{9}$ after simplification. 4. **Compare with $4:9$:** - $\frac{4}{9} \approx 0.444$. - $\frac{1}{3} \approx 0.333$ (not equal). - $\frac{25}{36} \approx 0.694$ (not equal). - $\frac{5}{6} \approx 0.833$ (not equal). - $\frac{4}{9} = 0.444$ (equal). 5. **Conclusion:** Only $36:81$ is equivalent to $4:9$. **Final answer:** $36:81$ is equivalent to $4:9$.