The perimeter of the square is 40 cm. A rectangle has the same width as the square. The length of the rectangle is double its width. The area (in `cm^(2)` ) of the rectangle is

Options

A. 150
B. 300
C. 350
D. 200

Answer

To solve the problem step by step, we will first determine the width of the square, then find the dimensions of the rectangle, and finally calculate the area of the rectangle.

### Step 1: Find the side length of the square
The formula for the perimeter \( P \) of a square is given by:
\[ P = 4 \times \text{side length} \]
Given that the perimeter of the square is 40 cm, we can set up the equation:
\[ 40 = 4 \times \text{side length} \]
To find the side length, divide both sides by 4:
\[ \text{side length} = \frac{40}{4} = 10 \text{ cm} \]

### Step 2: Determine the width of the rectangle
Since the rectangle has the same width as the square, the width of the rectangle is:
\[ \text{width} = 10 \text{ cm} \]

### Step 3: Calculate the length of the rectangle
The problem states that the length of the rectangle is double its width. Therefore, we can calculate the length as follows:
\[ \text{length} = 2 \times \text{width} = 2 \times 10 = 20 \text{ cm} \]

### Step 4: Calculate the area of the rectangle
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{width} \]
Substituting the values we found:
\[ A = 20 \times 10 = 200 \text{ cm}^2 \]

### Final Answer
The area of the rectangle is \( 200 \text{ cm}^2 \).

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