1. **Stating the problem:** We have two similar triangles, $\triangle JKL \sim \triangle QRS$. Given sides of $\triangle QRS$ are $QR=65$ and $RS=45$. For $\triangle JKL$, side $LK=72$ is given, and we need to find side $JK$. 2. **Using similarity ratios:** Since the triangles are similar, corresponding sides are proportional: $$\frac{JK}{QR} = \frac{LK}{RS}$$ 3. **Substitute known values:** $$\frac{JK}{65} = \frac{72}{45}$$ 4. **Simplify the right side fraction:** $$\frac{72}{45} = \frac{\cancel{72}^{24}}{\cancel{45}^{15}} = \frac{24}{15}$$ 5. **Solve for $JK$ by cross-multiplying:** $$JK = 65 \times \frac{24}{15}$$ 6. **Simplify the multiplication:** $$JK = 65 \times \frac{24}{15} = 65 \times \frac{8}{5}$$ 7. **Calculate the final value:** $$JK = 65 \times \frac{8}{5} = \cancel{65}^{13} \times 8 = 104$$ **Final answer:** $$JK = 104$$