Final answer:
For two rectangular lots each with an area of 432 square feet, the minimum amount of fencing required is approximately 103.9 feet, with the lots arranged as squares to minimize the perimeter.
Step-by-step explanation:
To find the minimum amount of fence needed to enclose two rectangular lots each containing 432 square feet, we must consider the dimensions that will minimize the perimeter. We can denote the length of the lot as L and the width of the lot as W, knowing that the area A is equal to L × W = 432 square feet.
For a rectangle, perimeter P is calculated as P = 2L + 2W. Since we need a fence across the middle, the total amount of fence F will be F = P + W. We need to minimize F considering A = 432.
In order to minimize the perimeter, L and W should be as close as possible to each other, which happens when the rectangle is a square. So, W = √432 = 20.78 feet (approx.) and L = √432 = 20.78 feet (approx.). Thus, P = 2×20.78 + 2×20.78 = 83.12 feet, and F = 83.12 + 20.78 = 103.9 feet (approx.). Therefore, the minimum amount of fencing required is approximately 103.9 feet.