The length of the diagonal of a square is `7sqrt(2)` cm . Then , the area of the square in `cm^(2)` is

Options

A. 28
B. `14sqrt(2)`
C. 21
D. 49

Answer

To find the area of the square given that the length of its diagonal is \(7\sqrt{2}\) cm, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the side of the square.
In a square, if \(x\) is the length of a side, the diagonal \(d\) can be expressed using the Pythagorean theorem:
\[ d = x\sqrt{2} \]

### Step 2: Substitute the given diagonal length into the equation.
We know that the diagonal \(d = 7\sqrt{2}\) cm. Therefore, we can set up the equation:
\[ 7\sqrt{2} = x\sqrt{2} \]

### Step 3: Solve for \(x\).
To isolate \(x\), we can divide both sides of the equation by \(\sqrt{2}\):
\[ x = 7 \]

### Step 4: Calculate the area of the square.
The area \(A\) of a square is given by the formula:
\[ A = x^2 \]
Substituting the value of \(x\):
\[ A = 7^2 = 49 \text{ cm}^2 \]

### Final Answer:
The area of the square is \(49 \text{ cm}^2\).

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