The diagonal of a square measures `6sqrt(2)` cm. The measure of the diagonal of a square whose area is twice that of the first square is :

Options

A. `6sqrt(2)` cm
B. `12sqrt(2)` cm
C. 12 cm
D. 6 cm

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the relationship between the diagonal and the side of a square.
The diagonal \( d \) of a square is related to its side length \( a \) by the formula:
\[ d = a\sqrt{2} \]

### Step 2: Use the given diagonal to find the side length of the first square.
Given that the diagonal of the first square is \( 6\sqrt{2} \) cm, we can set up the equation:
\[ 6\sqrt{2} = a\sqrt{2} \]
To find \( a \), divide both sides by \( \sqrt{2} \):
\[ a = 6 \text{ cm} \]

### Step 3: Calculate the area of the first square.
The area \( A \) of a square is given by:
\[ A = a^2 \]
Substituting the value of \( a \):
\[ A = 6^2 = 36 \text{ cm}^2 \]

### Step 4: Find the area of the second square.
The area of the second square is twice that of the first square:
\[ A_{second} = 2 \times 36 = 72 \text{ cm}^2 \]

### Step 5: Find the side length of the second square.
Let \( b \) be the side length of the second square. Using the area formula:
\[ b^2 = 72 \]
Taking the square root of both sides gives:
\[ b = \sqrt{72} = 6\sqrt{2} \text{ cm} \]

### Step 6: Calculate the diagonal of the second square.
Using the diagonal formula again:
\[ d_{second} = b\sqrt{2} \]
Substituting the value of \( b \):
\[ d_{second} = (6\sqrt{2})\sqrt{2} = 6 \times 2 = 12 \text{ cm} \]

### Final Answer:
The measure of the diagonal of the second square is \( 12 \) cm.