Answer: The corresponding side of the bigger triangle is 20 cm.
Let the required side be x cm. The ratio of the areas of similar triangles equals the ratio of the squares of corresponding sides:
\[\frac{x^2}{12^2} = \frac{225}{81}\] \[\frac{x}{12} = \frac{15}{9} = \frac{5}{3}\] \[x = \frac{5 \times 12}{3} = 20\]