1. **Stating the problem:** Solve for $x$ in the proportion $\frac{x}{12} = \frac{5}{10}$. 2. **Formula used:** For proportions $\frac{a}{b} = \frac{c}{d}$, cross-multiply to get $a \times d = b \times c$. 3. **Apply cross multiplication:** $$x \times 10 = 12 \times 5$$ 4. **Simplify the right side:** $$10x = 60$$ 5. **Solve for $x$ by dividing both sides by 10:** $$\cancel{10}x = \frac{60}{\cancel{10}}$$ $$x = 6$$ 6. **Answer:** $x = 6$. This means the unknown side length $x$ is 6 units.