1. **State the problem:** We have two similar triangular prisms with corresponding side lengths. The smaller prism has sides 3 mm, 5 mm, 6 mm, and an unknown side $x$ mm. The larger prism has sides 11 mm, 18 mm, and 24 mm. We need to find $x$ as a fraction in simplest form. 2. **Recall the property of similar shapes:** Corresponding sides of similar shapes are proportional. This means the ratio of any side in the smaller prism to the corresponding side in the larger prism is the same. 3. **Set up the ratios:** We know three pairs of corresponding sides: $$\frac{3}{11} = \frac{x}{?} = \frac{5}{18} = \frac{6}{24}$$ 4. **Find the common ratio:** Simplify the known ratios: $$\frac{5}{18} \approx 0.2778, \quad \frac{6}{24} = \frac{1}{4} = 0.25, \quad \frac{3}{11} \approx 0.2727$$ The closest consistent ratio is between $\frac{3}{11}$ and $\frac{5}{18}$, so we use these to find $x$. 5. **Use the ratio to find $x$:** Since $x$ corresponds to 18 mm in the larger prism, set up the proportion: $$\frac{x}{18} = \frac{3}{11}$$ 6. **Solve for $x$:** $$x = 18 \times \frac{3}{11} = \frac{54}{11}$$ 7. **Simplify the fraction:** $\frac{54}{11}$ is already in simplest form because 54 and 11 have no common factors other than 1. **Final answer:** $$x = \frac{54}{11}$$