The perimeter of the rectangular field is 480 meters and the ratio between the length and breadth is 5:3. Find the area of the field.

Options

A. 54000 `m^2`
B. 13500 `m^2`
C. 15000 `m^2`
D. 7200 `m^2`

Answer

To solve the problem step by step, we will follow the given information about the rectangular field:

1. **Understanding the Problem**: We know the perimeter of the rectangular field is 480 meters and the ratio of the length (L) to the breadth (B) is 5:3. We need to find the area of the field.

2. **Setting Up Variables**: Let the length be represented as \( L = 5x \) and the breadth as \( B = 3x \), where \( x \) is a common multiplier.

3. **Using the Perimeter Formula**: The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2(L + B) \]
Substituting the values we have:
\[ 480 = 2(5x + 3x) \]

4. **Simplifying the Equation**: This simplifies to:
\[ 480 = 2(8x) \]
\[ 480 = 16x \]

5. **Solving for x**: To find \( x \), divide both sides by 16:
\[ x = \frac{480}{16} = 30 \]

6. **Finding Length and Breadth**: Now we can find the length and breadth using the value of \( x \):
- Length \( L = 5x = 5 \times 30 = 150 \) meters
- Breadth \( B = 3x = 3 \times 30 = 90 \) meters

7. **Calculating the Area**: The area (A) of the rectangle is given by:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 150 \times 90 = 13500 \text{ m}^2 \]

8. **Final Answer**: The area of the rectangular field is \( 13500 \text{ m}^2 \).