The area of a square field is 0.5 hectare. The length of its diagonal is

Options

A. 100m
B. 50m
C. 250m
D. `50sqrt2m`

Answer

To find the length of the diagonal of a square field given its area, follow these steps:

### Step 1: Understand the area of a square
The area \( A \) of a square can be expressed in terms of its side length \( s \) as:
\[ A = s^2 \]

### Step 2: Convert the area from hectares to square meters
Given that the area of the square field is 0.5 hectares, we need to convert this to square meters. We know that:
\[ 1 \text{ hectare} = 10,000 \text{ square meters} \]
Thus,
\[ 0.5 \text{ hectares} = 0.5 \times 10,000 = 5,000 \text{ square meters} \]

### Step 3: Set up the equation for the side length
Now, we can set up the equation using the area:
\[ s^2 = 5,000 \]

### Step 4: Solve for the side length
To find the side length \( s \), take the square root of both sides:
\[ s = \sqrt{5,000} \]
Calculating this gives:
\[ s \approx 70.71 \text{ meters} \]

### Step 5: Calculate the diagonal of the square
The formula for the diagonal \( d \) of a square in terms of the side length \( s \) is:
\[ d = s\sqrt{2} \]
Substituting the value of \( s \):
\[ d = 70.71 \sqrt{2} \]
Calculating this gives:
\[ d \approx 70.71 \times 1.414 \approx 100 \text{ meters} \]

### Final Answer
The length of the diagonal of the square field is approximately \( 100 \) meters.

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