The area of a square is `50 cm^(2)`. The length of its diagonal is

Options

A. `5sqrt2 cm`
B. 10 cm
C. `10sqrt2 cm`
D. 8 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:
\[ A = a^2 \]
where \( a \) is the length of one side of the square.

2. **Set Up the Equation**:
Given that the area of the square is \( 50 \, \text{cm}^2 \), we can set up the equation:
\[ a^2 = 50 \]

3. **Solve for the Side Length**:
To find the length of the side \( a \), take the square root of both sides:
\[ a = \sqrt{50} \]

4. **Calculate the Diagonal**:
The diagonal \( d \) of a square can be found using the formula:
\[ d = a\sqrt{2} \]
Substitute \( a = \sqrt{50} \) into the diagonal formula:
\[ d = \sqrt{50} \cdot \sqrt{2} \]

5. **Simplify the Expression**:
Combine the square roots:
\[ d = \sqrt{50 \cdot 2} = \sqrt{100} \]

6. **Find the Value of the Diagonal**:
Calculate the square root:
\[ d = 10 \, \text{cm} \]

### Final Answer:
The length of the diagonal of the square is \( 10 \, \text{cm} \).