of a square field is `6050 m^(2)` . The length of its diagonal is

Options

A. 135m
B. 120m
C. 112m
D. 110m

Explanation

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

### Step 1: Understand the formula for 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: Relate the area to the diagonal
The diagonal \( d \) of a square can be related to its side length using the formula:
\[ d = s\sqrt{2} \]
We can also express the area in terms of the diagonal:
\[ A = \frac{1}{2} d^2 \]

### Step 3: Set up the equation
Given that the area of the square field is \( 6050 \, m^2 \), we can set up the equation:
\[ \frac{1}{2} d^2 = 6050 \]

### Step 4: Solve for \( d^2 \)
Multiply both sides of the equation by 2 to eliminate the fraction:
\[ d^2 = 6050 \times 2 \]
\[ d^2 = 12100 \]

### Step 5: Find \( d \) by taking the square root
Now, take the square root of both sides to find \( d \):
\[ d = \sqrt{12100} \]
Calculating the square root:
\[ d = 110 \, m \]

### Final Answer
The length of the diagonal of the square field is \( 110 \, m \).

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