1. The problem asks to find the length of side $x$ in parallelogram $EFGH$ given the sides of parallelogram $ABCD$ and some sides of $EFGH$. 2. We know that parallelograms that are similar have proportional corresponding sides. Here, $ABCD \sim EFGH$. 3. The sides of $ABCD$ are $AB = 1.2$ and $DC = 1.8$. The sides of $EFGH$ given are $FE = 0.4$ and $GH = x$. 4. Since $AB$ corresponds to $FE$ and $DC$ corresponds to $GH$, the ratio of corresponding sides is: $$\frac{AB}{FE} = \frac{DC}{GH}$$ 5. Substitute the known values: $$\frac{1.2}{0.4} = \frac{1.8}{x}$$ 6. Simplify the left side: $$\frac{1.2}{0.4} = 3$$ 7. So we have: $$3 = \frac{1.8}{x}$$ 8. Cross multiply to solve for $x$: $$3x = 1.8$$ 9. Divide both sides by 3: $$x = \frac{1.8}{3}$$ 10. Simplify the fraction: $$x = \frac{\cancel{1.8}}{\cancel{3}} = 0.6$$ 11. Therefore, the length of side $x$ is $0.6$. **Final answer:** $x = 0.6$