If the area of a square be 22050 sq. cm . Find the length of diagonal :

Options

A. 201 cm
B. 220 cm
C. 211 cm
D. 210 cm

Answer

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

### Step-by-Step Solution:

1. **Understand the relationship between area and side length of a square**:
The area \( A \) of a square is given by the formula:
\[ A = s^2 \]
where \( s \) is the length of one side of the square.

2. **Set up the equation using the given area**:
We know the area of the square is 22,050 sq. cm:
\[ s^2 = 22050 \]

3. **Solve for the side length \( s \)**:
To find \( s \), we take the square root of both sides:
\[ s = \sqrt{22050} \]

4. **Calculate the square root**:
We can simplify \( \sqrt{22050} \):
\[ \sqrt{22050} = 105\sqrt{2} \text{ cm} \]
(This can be calculated using a calculator or by prime factorization.)

5. **Use the formula for the diagonal of a square**:
The length of the diagonal \( d \) of a square can be found using the formula:
\[ d = s\sqrt{2} \]

6. **Substitute the value of \( s \)**:
Now substitute \( s = 105\sqrt{2} \) into the diagonal formula:
\[ d = (105\sqrt{2})\sqrt{2} \]

7. **Simplify the expression**:
\[ d = 105 \cdot 2 = 210 \text{ cm} \]

8. **Conclusion**:
The length of the diagonal of the square is:
\[ \boxed{210 \text{ cm}} \]