The diagonal of a square is `4sqrt(2) cm`. The diagonal of another square whose area is double that of the first square is

Options

A. 8 cm
B. `8//2 cm`
C. `4^2` cm
D. 6 cm

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the side length of the first square.
Given that the diagonal of the first square is \(4\sqrt{2}\) cm, we can use the relationship between the side length \(a\) of a square and its diagonal \(d\):
\[ d = a\sqrt{2} \]
Substituting the given diagonal:
\[ 4\sqrt{2} = a\sqrt{2} \]
To find \(a\), we can divide both sides by \(\sqrt{2}\):
\[ a = 4 \text{ cm} \]

### Step 2: Calculate the area of the first square.
The area \(A\) of a square is given by:
\[ A = a^2 \]
Substituting the side length we found:
\[ A = 4^2 = 16 \text{ cm}^2 \]

### Step 3: Determine the area of the second square.
The area of the second square is double that of the first square:
\[ A_{second} = 2 \times A_{first} = 2 \times 16 = 32 \text{ cm}^2 \]

### Step 4: Find the side length of the second square.
Let the side length of the second square be \(x\). The area of the second square can also be expressed as:
\[ A_{second} = x^2 \]
Setting this equal to the area we calculated:
\[ x^2 = 32 \]
Taking the square root of both sides:
\[ x = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \text{ cm} \]

### Step 5: Calculate the diagonal of the second square.
The diagonal \(d_{second}\) of the second square can be calculated using the side length \(x\):
\[ d_{second} = x\sqrt{2} = (4\sqrt{2})\sqrt{2} = 4 \times 2 = 8 \text{ cm} \]

### Final Answer:
The diagonal of the second square is \(8\) cm.

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