Problem 55

First, divide the perimeter by 2 and then by the sum of the ratio of length to width (1+3),
$= 36 \div 2 \div (1+3)$,
$= 18 \div 4$,
$= 4.5$ (meters),
The width is 4.5 meters, and since the length is three times the width, $4.5 \times 3 = 13.5$ (meters),
The area of the rectangle is $13.5 \times 4.5 = 60.75$ (square meters),
Answer: The area of this rectangle is $60.75$ square meters,
Therefore, the answer is $\boxed{60.75}$ square meters.
Given the perimeter of the rectangle is 36 meters, we know that the sum of length and width is $36 \div 2$. Based on "the length is three times the width," if we consider the width as one part, the length is three parts. From this, we can find one part and then calculate the length and width. Finally, using the formula for the area of a rectangle $S = ab$, we can find the area of this rectangle.
The key is to flexibly use the formula for the perimeter of a rectangle $C = (a+b) \times 2$ and the formula for the area of a rectangle $S = ab$ to solve the problem.