The difference between the length and breath of a rectangle is 6 m.
If its perimeter is 64 m , then its area is :
A.256 sq.m
B.247 sq.m
C. 264 sq.m
D. 238 sq.m

Options

A. A
B. B
C. D
D. C

Answer

To solve the problem step by step, we will use the given information about the rectangle's dimensions, perimeter, and area.

### Step 1: Define the Variables
Let:
- \( L \) = Length of the rectangle
- \( B \) = Breadth of the rectangle

### Step 2: Set Up the Equations
From the problem, we have two key pieces of information:
1. The difference between the length and breadth is 6 m:
\[ L - B = 6 \quad \text{(Equation 1)} \]
2. The perimeter of the rectangle is 64 m:
\[ 2(L + B) = 64 \quad \text{(Equation 2)} \]

### Step 3: Simplify the Perimeter Equation
From Equation 2, we can simplify it:
\[ L + B = \frac{64}{2} = 32 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
- \( L - B = 6 \) (Equation 1)
- \( L + B = 32 \) (Equation 3)

We can add these two equations together:
\[ (L - B) + (L + B) = 6 + 32 \]
This simplifies to:
\[ 2L = 38 \]
Dividing both sides by 2 gives:
\[ L = 19 \]

### Step 5: Find the Breadth
Now, substitute \( L = 19 \) back into Equation 1 to find \( B \):
\[ 19 - B = 6 \]
Rearranging gives:
\[ B = 19 - 6 = 13 \]

### Step 6: Calculate the Area
Now that we have both dimensions, we can calculate the area \( A \):
\[ A = L \times B = 19 \times 13 \]
Calculating this gives:
\[ A = 247 \, \text{sq.m} \]

### Conclusion
The area of the rectangle is \( 247 \, \text{sq.m} \). Therefore, the correct answer is option B: 247 sq.m.