1. **Problem Statement:** Solve the proportion $\frac{3}{5} = \frac{13}{x}$ to find the missing side length $x$. 2. **Formula Used:** For proportions, if $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$. 3. **Step-by-step Solution:** 1. Write the proportion: $$\frac{3}{5} = \frac{13}{x}$$ 2. Cross multiply: $$3 \times x = 5 \times 13$$ 3. Simplify multiplication: $$3x = 65$$ 4. Solve for $x$ by dividing both sides by 3: $$x = \frac{65}{3}$$ $$x = \cancel{\frac{65}{\cancel{3}}}$$ (no common factors to cancel here, so just division) 5. Calculate the decimal value: $$x \approx 21.67$$ 4. **Second proportion:** $\frac{13}{5} = \frac{x}{16}$ 1. Cross multiply: $$13 \times 16 = 5 \times x$$ 2. Simplify multiplication: $$208 = 5x$$ 3. Solve for $x$ by dividing both sides by 5: $$x = \frac{208}{5}$$ $$x = \cancel{\frac{208}{\cancel{5}}}$$ (no common factors to cancel here) 4. Calculate the decimal value: $$x = 41.6$$ **Final answers:** - From the first proportion, $x \approx 21.67$ - From the second proportion, $x = 41.6$