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

Options

A. 8 cm
B. `8 sqrt(2)` cm
C. 16 cm
D. `4 sqrt(2)` cm

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Find the area of the first square (S1)
Given that the diagonal (d1) of the first square is \(4\sqrt{2}\) cm, we can use the formula for the area of a square in terms of its diagonal:

\[ \text{Area} = \frac{d^2}{2} \]

Substituting the value of the diagonal:

\[ \text{Area of S1} = \frac{(4\sqrt{2})^2}{2} \]

Calculating \( (4\sqrt{2})^2 \):

\[ (4\sqrt{2})^2 = 16 \times 2 = 32 \]

Now substituting back into the area formula:

\[ \text{Area of S1} = \frac{32}{2} = 16 \text{ cm}^2 \]

### Step 2: Find the area of the second square (S2)
According to the problem, the area of the second square (S2) is double that of the first square (S1):

\[ \text{Area of S2} = 2 \times \text{Area of S1} = 2 \times 16 = 32 \text{ cm}^2 \]

### Step 3: Find the diagonal of the second square (S2)
Now we need to find the diagonal (d2) of the second square using the area formula again:

\[ \text{Area} = \frac{d^2}{2} \]

Setting the area of S2 equal to 32 cm²:

\[ \frac{d^2}{2} = 32 \]

Multiplying both sides by 2 to isolate \(d^2\):

\[ d^2 = 64 \]

Taking the square root of both sides to find d:

\[ d = \sqrt{64} = 8 \text{ cm} \]

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

---