A rectangle's length is 6 feet longer than three times its width. The rectangle's perimeter is 172 feet. Find the rectangle's length and width. The rectangle's length is $\square$ feet, and its width is $\square$ feet.

Step 1 ：The problem is asking for the length and width of a rectangle. We know that the perimeter of a rectangle is given by the formula \(2 \times (\text{length} + \text{width})\).

Step 2 ：We also know that the length of the rectangle is 6 feet longer than three times its width. This gives us the equation \(\text{length} = 3 \times \text{width} + 6\).

Step 3 ：We can set up a system of equations to solve for the length and width. The first equation will be from the given relationship between the length and width, and the second equation will be from the given perimeter.

Step 4 ：Solving this system of equations, we find that the width of the rectangle is 20 feet.

Step 5 ：Substituting the width into the equation for the length, we find that the length of the rectangle is 66 feet.

Step 6 ：Final Answer: The rectangle's length is \(\boxed{66}\) feet, and its width is \(\boxed{20}\) feet.