The diagonal of a square is 14 cm. What will be the length of the diagonal of the square whose area is double of the area of first square?

Options

A. `28sqrt2` cm
B. `14sqrt2` cm
C. 28 cm
D. `21sqrt2` cm

Answer

To find the length of the diagonal of a square whose area is double that of another square with a given diagonal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the diagonal of the first square**:
The diagonal of the first square is given as 14 cm.

2. **Use the relationship between the diagonal and the side of a square**:
The formula for the diagonal \(d\) of a square in terms of its side length \(a\) is:
\[ d = a\sqrt{2} \]
Therefore, we can express the side length \(a\) in terms of the diagonal:
\[ a = \frac{d}{\sqrt{2}} = \frac{14}{\sqrt{2}} = 7\sqrt{2} \text{ cm} \]

3. **Calculate the area of the first square**:
The area \(A\) of a square is given by:
\[ A = a^2 \]
Substituting the value of \(a\):
\[ A = (7\sqrt{2})^2 = 49 \times 2 = 98 \text{ cm}^2 \]

4. **Determine the area of the second square**:
The area of the second square is double that of the first square:
\[ A_{2} = 2 \times 98 = 196 \text{ cm}^2 \]

5. **Find the side length of the second square**:
Let \(b\) be the side length of the second square. Then:
\[ b^2 = 196 \implies b = \sqrt{196} = 14 \text{ cm} \]

6. **Calculate the diagonal of the second square**:
Using the diagonal formula again:
\[ d_{2} = b\sqrt{2} = 14\sqrt{2} \text{ cm} \]

### Final Answer:
The length of the diagonal of the square whose area is double that of the first square is \(14\sqrt{2}\) cm.

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