If the area of a rectangular field, whose dimensions are 64 m `xx` 36 m, is equal to the area of a square field, then the side of the square (in m.) is:

Options

A. 64
B. 48
C. 36
D. 24

Answer

To find the side of the square field that has the same area as the rectangular field with dimensions 64 m and 36 m, we can follow these steps:

### Step 1: Calculate the area of the rectangular field.
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]
Here, the length is 64 m and the breadth is 36 m.

\[ A = 64 \, \text{m} \times 36 \, \text{m} \]

### Step 2: Perform the multiplication.
Calculating the area:
\[ A = 64 \times 36 \]

To simplify:
\[ 64 \times 36 = 2304 \, \text{m}^2 \]

### Step 3: Set the area of the square equal to the area of the rectangle.
Let the side of the square be \( x \). The area of the square is given by:
\[ \text{Area of square} = x^2 \]
Since the area of the square is equal to the area of the rectangle, we have:
\[ x^2 = 2304 \]

### Step 4: Solve for \( x \) by taking the square root.
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{2304} \]

### Step 5: Calculate the square root.
Finding the square root:
\[ x = 48 \, \text{m} \]

### Conclusion:
The side of the square field is \( 48 \, \text{m} \).

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