1. **Problem Statement:** We have two rectangles. The larger rectangle has an area of $170$ square units and a height of $34$ units. The smaller rectangle has an area of $102$ square units. We need to find the width of the smaller rectangle. 2. **Formula Used:** Area of a rectangle is given by: $$\text{Area} = \text{width} \times \text{height}$$ 3. **Step 1: Find the width of the larger rectangle.** Given area $= 170$ and height $= 34$, we use: $$\text{width} = \frac{\text{Area}}{\text{height}} = \frac{170}{34} = 5$$ 4. **Step 2: Find the height of the smaller rectangle.** The smaller rectangle is adjacent vertically to the larger one, so its height is the difference between the total height and the height of the larger rectangle. Since the total height is not given explicitly, but the smaller rectangle is arranged to the right, we assume the height is the same as the larger rectangle's height, $34$ units. 5. **Step 3: Find the width of the smaller rectangle.** Given area $= 102$ and height $= 34$, we calculate: $$\text{width} = \frac{102}{34} = 3$$ 6. **Answer:** The width of the smaller rectangle is $3$ units. Therefore, the correct choice is **3**.