The area (in `m^(2)`) of the square which has the same perimeter as a rectangle whose length is 48 m and is 3 times its breadth, is :

Options

A. 1000
B. 1024
C. 1600
D. 1042

Answer

To solve the problem, we need to find the area of a square that has the same perimeter as a given rectangle. The rectangle has a length of 48 meters and its breadth is three times its breadth.

### Step-by-Step Solution:

1. **Identify the dimensions of the rectangle:**
- Given the length \( L = 48 \) m.
- Let the breadth be \( B \). According to the problem, the length is three times the breadth:
\[ L = 3B \]
- Substituting the value of \( L \):
\[ 48 = 3B \]
- Solving for \( B \):
\[ B = \frac{48}{3} = 16 \text{ m} \]

2. **Calculate the perimeter of the rectangle:**
- The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2(L + B) \]
- Substituting the values of \( L \) and \( B \):
\[ P = 2(48 + 16) = 2 \times 64 = 128 \text{ m} \]

3. **Determine the side length of the square:**
- The perimeter of a square is given by the formula:
\[ P = 4s \]
where \( s \) is the side length of the square.
- Since the perimeter of the square is equal to the perimeter of the rectangle:
\[ 4s = 128 \]
- Solving for \( s \):
\[ s = \frac{128}{4} = 32 \text{ m} \]

4. **Calculate the area of the square:**
- The area \( A \) of a square is given by:
\[ A = s^2 \]
- Substituting the value of \( s \):
\[ A = 32^2 = 1024 \text{ m}^2 \]

### Final Answer:
The area of the square is \( 1024 \, \text{m}^2 \).

---