1. The problem states that the area of a triangle is $\frac{25}{3}$ square centimeters and the height is $\frac{2}{5}$ cm. We need to find the length of the base. 2. Recall the formula for the area of a triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. Substitute the known values into the formula: $$\frac{25}{3} = \frac{1}{2} \times \text{base} \times \frac{2}{5}$$ 4. Simplify the right side: $$\frac{25}{3} = \frac{1}{2} \times \frac{2}{5} \times \text{base} = \frac{2}{10} \times \text{base} = \frac{1}{5} \times \text{base}$$ 5. So we have: $$\frac{25}{3} = \frac{1}{5} \times \text{base}$$ 6. To isolate the base, multiply both sides by 5: $$\text{base} = 5 \times \frac{25}{3}$$ 7. Multiply: $$\text{base} = \frac{125}{3}$$ 8. The base length expressed as a fraction in simplest form is $\frac{125}{3}$ cm.