To solve this problem, let's break it down step-by-step.

1. Initial Perimeter Formula:
   The perimeter $P$ of a rectangle is given by the formula: $P = 2L + 2W$ where $L$ is the length and $W$ is the width of the rectangle.

2. Scaling the Rectangle:
   If the length and width are scaled by a factor of 1.5, then the new length and new width are: $L' = 1.5L \quad \text{and} \quad W' = 1.5W$

3. Perimeter of the Scaled Rectangle:
   The perimeter of the new rectangle $P'$ is: $P' = 2L' + 2W' = 2(1.5L) + 2(1.5W) = 1.5(2L + 2W)$ This simplifies to: $P' = 1.5 \times P$

4. Substitute the Given Perimeter:
   The original perimeter $P$ is 48 ft. Therefore: $P' = 1.5 \times 48 = 72 \text{ ft}$

Thus, the perimeter of the resulting rectangle is 72 feet.

Would you like further details on how the scaling works or other related concepts?

Here are five related questions to explore:

1. How does scaling affect the area of a rectangle?
2. If the length and width were scaled by a factor of 2, how would the perimeter change?
3. What would the new area be if the perimeter is scaled by a factor of 1.5?
4. How would the perimeter change if the scaling factor was less than 1?
5. What is the relationship between the perimeter and area of similar rectangles?

Tip: When scaling geometric figures, the perimeter scales directly with the scaling factor, while the area scales with the square of that factor.