From the uploaded image, the question asks which answer choice correctly determines the width $w$ of a rectangle with an area of 48 square feet and a length of 12 feet.

The relationship for the area of a rectangle is:

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

Substitute the given values:

$48 = 12 \times w$

Solve for $w$:

$w = \frac{48}{12} = 4 \, \text{feet}$

The correct answer is the first option:

$12 \times w = 48 \quad \text{and} \quad w = 4 \, \text{feet}.$

Would you like further clarification on solving equations or interpreting the problem?

Here are 5 related questions to enhance understanding:

1. How can you verify the width of a rectangle if you know its area and length?
2. What are the units of measurement for area, length, and width?
3. What happens to the width if the area remains constant but the length changes?
4. Can a rectangle have the same area but different dimensions? Explain.
5. How would you solve for the length if the width and area were given instead?

Tip: Always double-check your solution by plugging it back into the original formula to confirm accuracy!