1. **State the problem:** We need to find the length of a rectangle given its perimeter and width. 2. **Given:** - Perimeter $P = 128.8$ - Width $W = 23.4$ 3. **Formula for perimeter of a rectangle:** $$P = 2(L + W)$$ where $L$ is the length and $W$ is the width. 4. **Substitute the known values:** $$128.8 = 2(L + 23.4)$$ 5. **Divide both sides by 2:** $$\frac{128.8}{2} = \cancel{2}(L + 23.4)/\cancel{2}$$ $$64.4 = L + 23.4$$ 6. **Solve for $L$ by subtracting 23.4 from both sides:** $$L = 64.4 - 23.4$$ $$L = 41$$ 7. **Answer:** The length of the rectangle is $41$. Only one answer is possible, which corresponds to option A.