To find the width of the floor, you can use the formula for the area of a rectangle:

$\text{Area} = \text{Length} \times \text{Width}$

Given that the area is $42 \, \text{m}^2$ and the length is $6 \, \text{m}$, you can rearrange the formula to solve for the width:

$\text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{42 \, \text{m}^2}{6 \, \text{m}} = 7 \, \text{m}$

So, the width of the floor is $7 \, \text{m}$.

If you want more details or have any questions, feel free to ask! Here are some related questions you might consider:

1. What are other methods to calculate the area of a rectangle?
2. How would the area change if the length were doubled?
3. Can you find the perimeter of the rectangle with these dimensions?
4. How does changing the width affect the area if the length remains constant?
5. What are the units of measurement commonly used in calculating areas?

Tip: Always double-check the units you are using in calculations to ensure consistency.