1. **State the problem:** We have two similar triangles with corresponding angle bisectors of lengths 3 and 5. The area of the smaller triangle is 45. We need to find the area of the larger triangle. 2. **Recall properties of similar triangles:** The ratio of corresponding linear elements (like angle bisectors) in similar triangles is equal to the ratio of their corresponding sides. 3. **Calculate the scale factor:** The ratio of the angle bisectors is $$\frac{5}{3}$$. 4. **Relate areas to scale factor:** The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides (or linear elements). So, $$\frac{\text{Area of larger triangle}}{\text{Area of smaller triangle}} = \left(\frac{5}{3}\right)^2 = \frac{25}{9}$$ 5. **Calculate the area of the larger triangle:** Given the smaller triangle's area is 45, $$\text{Area of larger triangle} = 45 \times \frac{25}{9} = 45 \times \frac{25}{9} = 5 \times 25 = 125$$ **Final answer:** The area of the larger triangle is 125.