There is rectangular parking lot with a length of 2x and a width of x. What is the ratio of the perimeter of the parking lot to the area of parking lot, in terms of x?

Answer

To find the ratio of the perimeter of a rectangular parking lot to its area, we will follow these steps:

### Step 1: Identify the dimensions of the rectangle
The length (l) of the parking lot is given as \(2x\) and the width (w) is given as \(x\).

### Step 2: Calculate the perimeter of the rectangle
The formula for the perimeter (P) of a rectangle is:
\[ P = 2 \times (l + w) \]
Substituting the values of length and width:
\[ P = 2 \times (2x + x) = 2 \times (3x) = 6x \]

### Step 3: Calculate the area of the rectangle
The formula for the area (A) of a rectangle is:
\[ A = l \times w \]
Substituting the values of length and width:
\[ A = 2x \times x = 2x^2 \]

### Step 4: Find the ratio of the perimeter to the area
Now, we need to find the ratio of the perimeter to the area:
\[ \text{Ratio} = \frac{P}{A} = \frac{6x}{2x^2} \]
Simplifying this expression:
\[ \text{Ratio} = \frac{6x}{2x^2} = \frac{6}{2x} = \frac{3}{x} \]

### Final Answer
The ratio of the perimeter of the parking lot to the area of the parking lot is:
\[ \frac{3}{x} \]

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