A square field of 2sq. Km is to be divided into two equal parts by a wall which coincides with a diagonal. Find the length of the wall :

Options

A. `sqrt(2)` km
B. 1 km
C. 4.2 km
D. 2 km

Answer

To find the length of the wall that divides a square field of 2 square kilometers into two equal parts along its diagonal, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Area of the Square Field**:
The area of the square field is given as 2 square kilometers.

2. **Calculate the Side Length of the Square**:
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Therefore, we can find the side length \( s \) by rearranging the formula:
\[ s = \sqrt{A} = \sqrt{2} \text{ km} \]

3. **Find the Length of the Diagonal**:
The diagonal \( d \) of a square can be calculated using the formula:
\[ d = s\sqrt{2} \]
Substituting the value of \( s \):
\[ d = \sqrt{2} \cdot \sqrt{2} = 2 \text{ km} \]

4. **Conclusion**:
The length of the wall that coincides with the diagonal of the square field is 2 kilometers.

### Final Answer:
The length of the wall is **2 km**.

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