1. **State the problem:** A photograph measures 11 inches wide and 14 inches long. It is enlarged so that the new width is 231 inches. We need to find the new length. 2. **Formula used:** When enlarging a picture proportionally, the ratio of width to length remains the same. So, we use the proportion: $$\frac{\text{original width}}{\text{original length}} = \frac{\text{new width}}{\text{new length}}$$ 3. **Set up the proportion:** $$\frac{11}{14} = \frac{231}{L}$$ where $L$ is the new length. 4. **Solve for $L$:** Cross-multiply: $$11 \times L = 14 \times 231$$ 5. **Calculate the right side:** $$14 \times 231 = 3234$$ 6. **Isolate $L$:** $$L = \frac{3234}{11}$$ 7. **Simplify the fraction:** $$L = \frac{\cancel{3234}}{\cancel{11}} = 294$$ 8. **Answer:** The new length is **294 inches**. This matches the third choice.