The length and perimeter of a rectangle are in the ratio of `5:18`. What will be the ratio of its length and breadth?

Options

A. `4 : 3`
B. `3 : 5`
C. `5 : 4`
D. `4 : 7`

Answer

To solve the problem step by step, we need to find the ratio of the length and breadth of a rectangle given that the length and perimeter are in the ratio of 5:18.

### Step-by-Step Solution:

1. **Understand the given ratio**:
We know that the ratio of the length (L) to the perimeter (P) of the rectangle is given as:
\[ \frac{L}{P} = \frac{5}{18} \]

2. **Write the formula for perimeter**:
The formula for the perimeter of a rectangle is:
\[ P = 2(L + B) \]
where B is the breadth of the rectangle.

3. **Substitute the perimeter formula into the ratio**:
We can substitute the formula for perimeter into our ratio:
\[ \frac{L}{2(L + B)} = \frac{5}{18} \]

4. **Cross-multiply to eliminate the fraction**:
Cross-multiplying gives us:
\[ 18L = 5 \cdot 2(L + B) \]
Simplifying this, we have:
\[ 18L = 10(L + B) \]

5. **Distribute on the right side**:
Expanding the right side:
\[ 18L = 10L + 10B \]

6. **Rearrange the equation**:
Move all terms involving L to one side:
\[ 18L - 10L = 10B \]
This simplifies to:
\[ 8L = 10B \]

7. **Express L in terms of B**:
To find the ratio of L to B, we can rearrange this equation:
\[ \frac{L}{B} = \frac{10}{8} \]

8. **Simplify the ratio**:
Simplifying \(\frac{10}{8}\) gives:
\[ \frac{L}{B} = \frac{5}{4} \]

9. **Final result**:
Therefore, the ratio of the length to the breadth of the rectangle is:
\[ L:B = 5:4 \]

### Conclusion:
The ratio of the length to the breadth of the rectangle is \(5:4\).