1. **State the problem:** We have two similar quadrilaterals. The left quadrilateral has a bottom side of 60 mm and a right side of 40 mm. The right quadrilateral is similar, with a corresponding side of 42 mm and a missing side length $w$ to find. 2. **Recall the property of similar figures:** Corresponding sides of similar figures are proportional. This means the ratios of corresponding side lengths are equal. 3. **Set up the proportion:** Let the side corresponding to 40 mm be $w$ in the smaller figure, and the side corresponding to 60 mm be 42 mm. $$\frac{w}{40} = \frac{42}{60}$$ 4. **Solve for $w$:** Cross multiply: $$w \times 60 = 42 \times 40$$ $$60w = 1680$$ Divide both sides by 60: $$w = \frac{1680}{60}$$ Show cancellation: $$w = \frac{\cancel{1680}}{\cancel{60}} = 28$$ 5. **Answer:** The missing length $w$ is 28 millimeters. This means the smaller quadrilateral's side corresponding to 40 mm in the larger figure measures 28 mm.