The area of a square is 100 sq. cm. Find length of its diagonal ?

Options

A. `10sqrt(2) cm`
B. 10 cm
C. 20 cm
D. `20sqrt(2) 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 Area 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. **Given Area**:
We are given that the area of the square is \( 100 \, \text{sq. cm} \). Therefore, we can set up the equation:
\[ s^2 = 100 \]

3. **Calculate the Side Length**:
To find the length of the side \( s \), we take the square root of both sides:
\[ s = \sqrt{100} = 10 \, \text{cm} \]

4. **Diagonal of the Square**:
The diagonal \( D \) of a square can be calculated using the formula:
\[ D = s\sqrt{2} \]
Substituting the value of \( s \):
\[ D = 10\sqrt{2} \, \text{cm} \]

5. **Final Answer**:
Thus, the length of the diagonal of the square is:
\[ D = 10\sqrt{2} \, \text{cm} \]