1. **State the problem:** We have two similar triangles DAR and KMR. We know side lengths DA = 16, DR = 11, MR = 14, and we want to find the unknown side length $y = KR$ in triangle KMR. 2. **Recall the property of similar triangles:** Corresponding sides of similar triangles are proportional. This means: $$\frac{DA}{KM} = \frac{DR}{MR} = \frac{AR}{KR}$$ 3. **Identify corresponding sides:** From the problem, $DA$ corresponds to $KM$, $DR$ corresponds to $MR$, and $AR$ corresponds to $KR = y$. 4. **Set up the proportion using known sides:** $$\frac{DA}{KM} = \frac{DR}{MR}$$ Substitute known values: $$\frac{16}{y} = \frac{11}{14}$$ 5. **Solve for $y$:** Cross multiply: $$16 \times 14 = 11 \times y$$ $$224 = 11y$$ Divide both sides by 11: $$y = \frac{224}{11}$$ Show cancellation: $$y = \frac{\cancel{224}}{\cancel{11}}$$ 6. **Calculate the value:** $$y \approx 20.36$$ **Final answer:** $$\boxed{y \approx 20.36}$$ This means the side $KR$ in triangle KMR is approximately 20.36 units long.