The area of a square is equal to four times the area of a rectangle of dimensions 256cm * 64cm. what is the perimeter of the square?

Options

A. a. 600cm
B. b. 1024cm
C. c. 400cm
D. d.none of these

Answer

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

### Step 1: Calculate the area of the rectangle
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{length} \times \text{width} \]
Given the dimensions of the rectangle are 256 cm and 64 cm, we can calculate the area as follows:
\[ \text{Area of rectangle} = 256 \, \text{cm} \times 64 \, \text{cm} \]

### Step 2: Calculate the area of the rectangle
Now, let's perform the multiplication:
\[ \text{Area of rectangle} = 256 \times 64 = 16384 \, \text{cm}^2 \]

### Step 3: Calculate the area of the square
According to the problem, the area of the square is equal to four times the area of the rectangle:
\[ \text{Area of square} = 4 \times \text{Area of rectangle} = 4 \times 16384 \, \text{cm}^2 \]

### Step 4: Calculate the area of the square
Now, let's calculate the area of the square:
\[ \text{Area of square} = 4 \times 16384 = 65536 \, \text{cm}^2 \]

### Step 5: Find the side length of the square
The area of a square is also given by the formula:
\[ \text{Area} = \text{side}^2 \]
We can set this equal to the area we just calculated:
\[ \text{side}^2 = 65536 \]
To find the side length, we take the square root:
\[ \text{side} = \sqrt{65536} \]

### Step 6: Calculate the side length
Calculating the square root:
\[ \text{side} = 256 \, \text{cm} \]

### Step 7: Calculate the perimeter of the square
The perimeter of a square is given by the formula:
\[ \text{Perimeter} = 4 \times \text{side} \]
Substituting the side length we found:
\[ \text{Perimeter} = 4 \times 256 \, \text{cm} \]

### Step 8: Calculate the perimeter
Now, let's calculate the perimeter:
\[ \text{Perimeter} = 1024 \, \text{cm} \]

### Final Answer
The perimeter of the square is \(1024 \, \text{cm}\).

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