1. **Problem:** The ratio between two corresponding sides in two similar triangles is 4 : 3 and the perimeter of the smaller triangle is 36 cm. Find the perimeter of the greater triangle. 2. **Formula and Rules:** - For similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides. - If the ratio of sides is $\frac{4}{3}$, then the ratio of perimeters is also $\frac{4}{3}$. 3. **Work:** - Let the perimeter of the greater triangle be $P$. - Given the smaller triangle perimeter = 36 cm. - Using the ratio: $$\frac{P}{36} = \frac{4}{3}$$ - Multiply both sides by 36: $$P = 36 \times \frac{4}{3}$$ - Simplify: $$P = 36 \times \frac{4}{3} = 36 \times \frac{4}{3} = 12 \times 4 = 48$$ 4. **Answer:** The perimeter of the greater triangle is **48 cm**.