1. **State the problem:** We want to understand why the variable $x$, representing the side length of squares cut from each corner of a 30 cm by 20 cm cardboard, must be less than 10 cm. 2. **Recall the setup:** Squares of side length $x$ are cut from each corner, and the sides are folded up to form a box. 3. **Reasoning about $x$:** Since squares are cut from both ends of the width (which is 20 cm), the total length removed from the width is $2x$. 4. **Constraint on width after cutting:** The new width after cutting is $20 - 2x$. 5. **Physical feasibility:** For the box to exist, the width must be positive: $$20 - 2x > 0$$ 6. **Solve inequality:** $$20 > 2x$$ $$\Rightarrow 10 > x$$ 7. **Conclusion:** Therefore, $x$ must be less than 10 cm to ensure the width remains positive and the box can be formed physically.