The ratio between the perimeter and the length of a rectangle is 5:2. Find the ratio between the length and the breadth of the rectangle.

Answer

To solve the problem step by step, we will follow the given information and use the formula for the perimeter of a rectangle.

### Step-by-Step Solution:

1. **Understand the Problem**: We know that the ratio between the perimeter (P) and the length (L) of a rectangle is given as 5:2. We need to find the ratio between the length (L) and the breadth (B) of the rectangle.

2. **Recall the Perimeter Formula**: The formula for the perimeter of a rectangle is:
\[ P = 2(L + B) \]

3. **Set Up the Ratio**: According to the problem, we have:
\[ \frac{P}{L} = \frac{5}{2} \]
This can be rewritten as:
\[ P = \frac{5}{2}L \]

4. **Substitute the Perimeter Formula**: Now, substitute the formula for the perimeter into the equation:
\[ 2(L + B) = \frac{5}{2}L \]

5. **Clear the Fraction**: To eliminate the fraction, multiply both sides of the equation by 2:
\[ 4(L + B) = 5L \]

6. **Distribute and Rearrange**: Distributing on the left side gives:
\[ 4L + 4B = 5L \]
Now, rearranging the equation to isolate terms involving B:
\[ 4B = 5L - 4L \]
This simplifies to:
\[ 4B = L \]

7. **Find the Ratio**: Now, we need to find the ratio of length (L) to breadth (B):
\[ \frac{L}{B} = \frac{4B}{B} = 4:1 \]

8. **Final Answer**: Therefore, the ratio between the length and the breadth of the rectangle is:
\[ \text{Length : Breadth} = 4 : 1 \]