1. **Problem Statement:** We have a 3 × 4 rectangle made of identical sticks. We want to find how many sticks are needed to construct a 40 × 50 rectangle. 2. **Understanding the problem:** The sticks form the grid lines of the rectangle. For a grid of $m$ rows and $n$ columns, the number of sticks is the sum of the horizontal and vertical sticks. 3. **Formula for sticks in a grid:** - Horizontal sticks: $(m+1) \times n$ - Vertical sticks: $m \times (n+1)$ - Total sticks: $$\text{Total} = (m+1) \times n + m \times (n+1)$$ 4. **Apply to the 3 × 4 rectangle:** - Horizontal sticks: $(3+1) \times 4 = 4 \times 4 = 16$ - Vertical sticks: $3 \times (4+1) = 3 \times 5 = 15$ - Total sticks: $16 + 15 = 31$ 5. **Apply to the 40 × 50 rectangle:** - Horizontal sticks: $(40+1) \times 50 = 41 \times 50 = 2050$ - Vertical sticks: $40 \times (50+1) = 40 \times 51 = 2040$ - Total sticks: $2050 + 2040 = 4090$ 6. **Answer:** The number of sticks needed is **4090**, which corresponds to option (C).