1. **State the problem:** We need to find the perimeter of a parallelogram with sides measuring $1 \frac{1}{4}$ km and $1 \frac{1}{5}$ km. 2. **Recall the formula:** The perimeter $P$ of a parallelogram is given by $$P = 2(\text{length} + \text{width})$$ 3. **Convert mixed numbers to improper fractions:** - $1 \frac{1}{4} = \frac{5}{4}$ - $1 \frac{1}{5} = \frac{6}{5}$ 4. **Add the side lengths:** $$\frac{5}{4} + \frac{6}{5} = \frac{5 \times 5}{4 \times 5} + \frac{6 \times 4}{5 \times 4} = \frac{25}{20} + \frac{24}{20} = \frac{49}{20}$$ 5. **Multiply by 2 to find the perimeter:** $$P = 2 \times \frac{49}{20} = \frac{98}{20}$$ 6. **Simplify the fraction:** $$\frac{98}{20} = \frac{49}{10} = 4 \frac{9}{10}$$ **Final answer:** The perimeter is $4 \frac{9}{10}$ kilometers.