Area ofrece angular field is `3584 m^2` and the length and the breadth are in the ratio 7 : 2 respectively. What is the perimeter of the rectangle ?

Options

A. 246 m
B. 292 m
C. 286 m
D. 288 m

Explanation

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

### Step 1: Understand the problem
We know the area of the rectangular field is \( 3584 \, m^2 \) and the ratio of length (L) to breadth (B) is \( 7:2 \).

### Step 2: Set up the equations
Let the length be \( 7x \) and the breadth be \( 2x \). The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Substituting the values we have:
\[ 3584 = (7x) \times (2x) \]

### Step 3: Simplify the equation
This simplifies to:
\[ 3584 = 14x^2 \]

### Step 4: Solve for \( x^2 \)
To find \( x^2 \), divide both sides by 14:
\[ x^2 = \frac{3584}{14} \]
Calculating the right side:
\[ x^2 = 256 \]

### Step 5: Find \( x \)
Taking the square root of both sides gives:
\[ x = \sqrt{256} = 16 \]

### Step 6: Calculate Length and Breadth
Now, we can find the length and breadth:
\[ L = 7x = 7 \times 16 = 112 \, m \]
\[ B = 2x = 2 \times 16 = 32 \, m \]

### Step 7: Calculate the Perimeter
The perimeter \( P \) of a rectangle is given by:
\[ P = 2(L + B) \]
Substituting the values we found:
\[ P = 2(112 + 32) = 2 \times 144 = 288 \, m \]

### Final Answer
The perimeter of the rectangle is \( 288 \, m \).

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