The ratio between the breadth and the perimeter of a rectangle is 2:10. Find the ratio between the length and the breadth of the rectangle.

Answer

To find the ratio between the length and breadth of a rectangle given that the ratio between the breadth and the perimeter is 2:10, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship given in the problem:**
The ratio of breadth (B) to perimeter (P) is given as 2:10. This can be expressed as:
\[ \frac{B}{P} = \frac{2}{10} \]

2. **Express the perimeter in terms of length (L) and breadth (B):**
The formula for the perimeter of a rectangle is:
\[ P = 2(L + B) \]

3. **Substitute the perimeter formula into the ratio:**
Replace P in the ratio with the formula:
\[ \frac{B}{2(L + B)} = \frac{2}{10} \]

4. **Cross-multiply to eliminate the fraction:**
Cross-multiplying gives:
\[ 10B = 4(L + B) \]

5. **Distribute on the right side:**
Expanding the equation results in:
\[ 10B = 4L + 4B \]

6. **Rearrange the equation to isolate terms involving L and B:**
Move all terms involving B to one side:
\[ 10B - 4B = 4L \]
This simplifies to:
\[ 6B = 4L \]

7. **Divide both sides by 2 to simplify:**
\[ 3B = 2L \]

8. **Rearrange to find the ratio of length to breadth:**
Dividing both sides by B gives:
\[ \frac{L}{B} = \frac{3}{2} \]

9. **Express the ratio in the standard form:**
The ratio of length to breadth is:
\[ L:B = 3:2 \]

### Final Answer:
The ratio between the length and breadth of the rectangle is \( 3:2 \).