To rearrange the formula for the volume of a box, represented as \( v = lwh \), to solve for the width \( w \), you can isolate \( w \) on one side of the equation.
Start with the original equation:
\[ v = lwh \]
To solve for \( w \), divide both sides by \( l \) and \( h \):
\[ w = \frac{v}{lh} \]
This equation shows that the width \( w \) is equal to the volume \( v \) divided by the product of the length \( l \) and the height \( h \).
In this context, the units for each variable are as follows:
- Volume \( v \) is measured in cubic units (e.g., cubic meters, cubic centimeters),
- Length \( l \) and height \( h \) are measured in linear units (e.g., meters, centimeters).
Therefore, the units for \( w \) can be derived as follows:
\[ \text{units of } w = \frac{\text{units of } v}{\text{units of } l \times \text{units of } h} = \frac{\text{cubic units}}{\text{linear units} \times \text{linear units}} = \frac{\text{cubic units}}{\text{square units}} = \text{linear units} \]
Thus, the unit analysis confirms that the width \( w \) will retain the dimensions of length, validating the rearrangement of the original volume formula.
In summary, the equation that best represents the meaning unit when justifying your rearrangement to solve for width is:
\[ w = \frac{v}{lh} \]
With the understanding that the units of \( w \) appropriately derive from the division of volume by the product of two lengths.