1. **State the problem:** We need to find the length of a billboard given its area and width. 2. **Given:** - Area $A = 31 \frac{1}{2} = 31.5$ square yards - Width $w = 4 \frac{1}{2} = 4.5$ yards 3. **Formula:** The area of a rectangle is given by $$A = \text{length} \times \text{width}$$ Let the length be $L$. Then, $$31.5 = L \times 4.5$$ 4. **Solve for length:** $$L = \frac{31.5}{4.5}$$ 5. **Calculate:** $$L = 7$$ 6. **Answer:** The length of the billboard is $7$ yards.