Given that the area $A$ of the rectangle is 30 square feet, we can express the perimeter $P$ of the rectangle as a function of its width $w$.

1. Area formula: $A = l \times w$ where $l$ is the length and $w$ is the width. Since $A = 30$ square feet, we have: $l \times w = 30$ Therefore, the length $l$ can be expressed as: $l = \frac{30}{w}$

2. Perimeter formula: The perimeter $P$ of a rectangle is given by: $P = 2l + 2w$ Substituting $l = \frac{30}{w}$ into the perimeter formula: $P = 2\left(\frac{30}{w}\right) + 2w$ Simplifying: $P = \frac{60}{w} + 2w$

Thus, the perimeter $P$ as a function of width $w$ is: $P(w) = \frac{60}{w} + 2w$

Would you like more details or further explanation on any step?

Here are some related questions for further exploration:

1. What is the perimeter of the rectangle if the width is 5 feet?
2. How does the function behave as the width becomes very small?
3. How does the function behave as the width becomes very large?
4. How can we find the minimum perimeter for this rectangle?
5. What are the dimensions of the rectangle if the perimeter is 40 feet?

Tip: When working with perimeter and area formulas, it's helpful to remember the geometric relationships between the dimensions of the shapes!