1. **State the problem:** We have two similar quadrilaterals. The smaller one has side lengths 3 inches and 1 inch, and the larger one has corresponding side lengths 2 inches and an unknown length $w$. We need to find $w$. 2. **Recall the property of similar shapes:** Corresponding sides of similar shapes are proportional. This means the ratio of one pair of corresponding sides equals the ratio of the other pair. 3. **Set up the proportion:** The side labeled 2 inches corresponds to the side labeled 3 inches, and the side labeled $w$ corresponds to the side labeled 1 inch. So, $$\frac{2}{3} = \frac{w}{1}$$ 4. **Solve for $w$:** Multiply both sides by 1 (which does not change the value), so $$w = \frac{2}{3}$$ 5. **Interpret the result:** The missing length $w$ is $\frac{2}{3}$ inches, or approximately 0.67 inches. **Final answer:** $$w = \frac{2}{3} \text{ inches}$$