The area of a square is `200 cm^(2)`. The length of its diagonal is

Options

A. 10cm
B. 20cm
C. `10sqrt2cm`
D. 14.1cm

Answer

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

### Step 1: Understand the relationship between the area and the side of the square.
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Given that the area of the square is \( 200 \, \text{cm}^2 \), we can set up the equation:
\[ \text{side}^2 = 200 \]

### Step 2: Solve for the side of the square.
To find the side length, we take the square root of both sides:
\[ \text{side} = \sqrt{200} \]
We can simplify \( \sqrt{200} \):
\[ \sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2} \, \text{cm} \]

### Step 3: Use the side length to find the diagonal.
The diagonal \( d \) of a square can be calculated using the formula:
\[ d = \text{side} \times \sqrt{2} \]
Substituting the value of the side:
\[ d = 10\sqrt{2} \times \sqrt{2} \]
This simplifies to:
\[ d = 10 \times 2 = 20 \, \text{cm} \]

### Conclusion
The length of the diagonal of the square is \( 20 \, \text{cm} \).

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