`{:("Column A","The perimeter of rectangle ABCD is 5/2 times as long as the side AB","Column B"),("Length of side AB",,"Length of side BC"):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to analyze the relationship between the sides of rectangle ABCD based on the given information about its perimeter.

### Step-by-Step Solution:

1. **Define the sides of the rectangle**:
Let the length of side AB be denoted as \( X \) and the length of side BC be denoted as \( Y \).

2. **Write the formula for the perimeter of a rectangle**:
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (L + B) = 2 \times (X + Y) \]

3. **Set up the equation based on the given information**:
According to the problem, the perimeter of rectangle ABCD is \( \frac{5}{2} \) times the length of side AB. Therefore, we can write:
\[ 2 \times (X + Y) = \frac{5}{2} \times X \]

4. **Simplify the equation**:
We can simplify the equation:
\[ 2X + 2Y = \frac{5}{2}X \]
To eliminate the fraction, multiply the entire equation by 2:
\[ 4X + 4Y = 5X \]

5. **Rearranging the equation**:
Rearranging gives us:
\[ 4Y = 5X - 4X \]
\[ 4Y = X \]

6. **Express Y in terms of X**:
Dividing both sides by 4, we find:
\[ Y = \frac{1}{4}X \]

7. **Compare the lengths of sides AB and BC**:
Since \( AB = X \) and \( BC = Y \), we can express the relationship:
\[ AB = 4 \times BC \]
This shows that the length of side AB is greater than the length of side BC.

### Conclusion:
From the analysis, we conclude that the length of side AB is greater than the length of side BC. Therefore, the answer to the comparison in the columns is that Column A (Length of side AB) is greater than Column B (Length of side BC).