Let's break this down step by step:

1. Picture Description: You want to enclose a rectangular field using 16 miles of fence. Suppose you arrange it into a rectangle with a width of 3 miles and a length of 5 miles.

   • The total perimeter $P$ of the rectangle is the sum of all sides: $P = 2(\text{Length}) + 2(\text{Width})$
   • Substituting the given values: $P = 2(5) + 2(3) = 10 + 6 = 16 \text{ miles}$ This confirms that the fence can indeed form a rectangle of length 5 miles and width 3 miles.

2. Area Calculation: The area $A$ of the rectangle is given by: $A = \text{Length} \times \text{Width} = 5 \times 3 = 15 \text{ square miles}$

So, the area of the rectangle is 15 square miles.

Would you like a more detailed explanation or a visual diagram of this setup?

Related Questions:

1. What if the width is 4 miles? What would the corresponding length be?
2. How does the area change if you increase the width to 4 miles while keeping the perimeter constant?
3. What is the maximum area you can enclose with 16 miles of fencing?
4. Can you express the area as a function of one variable, say the width?
5. How would the formula for the perimeter change if it were an irregular quadrilateral?

Tip: For a fixed perimeter, a square encloses the maximum area among rectangles.