1. **State the problem:** We have a rectangle with width $3$ units and an unknown length $L$ units. The problem states that the perimeter and the area of the rectangle have the same numerical value. We need to find the length $L$. 2. **Recall formulas:** - Perimeter of a rectangle: $$P = 2(\text{length} + \text{width}) = 2(L + 3)$$ - Area of a rectangle: $$A = \text{length} \times \text{width} = L \times 3 = 3L$$ 3. **Set up the equation:** Since the perimeter equals the area, we have: $$2(L + 3) = 3L$$ 4. **Solve the equation:** $$2L + 6 = 3L$$ Subtract $2L$ from both sides: $$6 = 3L - 2L$$ $$6 = L$$ 5. **Interpret the result:** The length of the rectangle is $6$ units. **Final answer:** The length of the rectangle is $6$ units.