The area of rectangle is `450cm^2` which is 50% of the area of a square. What is the perimeter of the square?

Options

A. 80 cm
B. 160 cm
C. 40 cm
D. 120cm

Answer

To find the perimeter of the square given that the area of the rectangle is 450 cm² and that this area is 50% of the area of the square, we can follow these steps:

### Step 1: Find the area of the square
We know that the area of the rectangle is 450 cm² and this is 50% of the area of the square. Therefore, we can set up the equation:

\[ \text{Area of square} = \frac{\text{Area of rectangle}}{0.5} \]

Substituting the area of the rectangle:

\[ \text{Area of square} = \frac{450 \text{ cm}^2}{0.5} = 900 \text{ cm}^2 \]

### Step 2: Find the side length of the square
The area of a square is given by the formula:

\[ \text{Area} = \text{side}^2 \]

Let the side length of the square be \( s \). Therefore, we have:

\[ s^2 = 900 \]

To find \( s \), we take the square root of both sides:

\[ s = \sqrt{900} = 30 \text{ cm} \]

### Step 3: Calculate the perimeter of the square
The perimeter \( P \) of a square is given by the formula:

\[ P = 4 \times \text{side} \]

Substituting the value of the side:

\[ P = 4 \times 30 \text{ cm} = 120 \text{ cm} \]

### Final Answer
The perimeter of the square is \( 120 \text{ cm} \).

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