The perimeter of a rectangular field is 240 m and the ratio between the length and breadth is 5: 3 . What is the area of field?

Options

A. ` 3370 m ^(2)`
B. ` 3735 m ^(2)`
C. ` 3375 m ^(2) `
D. None of these

Answer

To find the area of the rectangular field given the perimeter and the ratio of length to breadth, we can follow these steps:

### Step 1: Understand the given information
We know:
- The perimeter of the rectangular field is 240 m.
- The ratio of length (L) to breadth (B) is 5:3.

### Step 2: Set up the equations
Let the length be represented as \( L = 5x \) and the breadth as \( B = 3x \), where \( x \) is a common multiplier.

### Step 3: Write the formula for the perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2(L + B) \]
Substituting the expressions for length and breadth, we get:
\[ 240 = 2(5x + 3x) \]

### Step 4: Simplify the equation
Combine the terms inside the parentheses:
\[ 240 = 2(8x) \]
This simplifies to:
\[ 240 = 16x \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 16:
\[ x = \frac{240}{16} = 15 \]

### Step 6: Find the length and breadth
Now substitute \( x \) back into the expressions for length and breadth:
\[ L = 5x = 5 \times 15 = 75 \, \text{m} \]
\[ B = 3x = 3 \times 15 = 45 \, \text{m} \]

### Step 7: Calculate the area
The area \( A \) of the rectangle is given by:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 75 \times 45 \]

### Step 8: Perform the multiplication
Calculating \( 75 \times 45 \):
\[ A = 3375 \, \text{m}^2 \]

### Final Answer
The area of the rectangular field is \( 3375 \, \text{m}^2 \).

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