A square has the same area as that of a rectangle. The length and the breadth of the rectangle are 9cm and 4cm, respectively.
Calculate the perimeter of the square.

Answer

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

### Step 1: Calculate the Area of the Rectangle
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 9 cm
- Breadth = 4 cm

Now, substituting the values:
\[ \text{Area} = 9 \, \text{cm} \times 4 \, \text{cm} = 36 \, \text{cm}^2 \]

### Step 2: Set the Area of the Square Equal to the Area of the Rectangle
We know that the area of the square is equal to the area of the rectangle. Therefore:
\[ \text{Area of Square} = \text{Area of Rectangle} = 36 \, \text{cm}^2 \]

### Step 3: Use the Area of the Square to Find the Side Length
The area of a square is given by the formula:
\[ \text{Area} = \text{Side}^2 \]
Setting this equal to the area we found:
\[ \text{Side}^2 = 36 \, \text{cm}^2 \]
To find the side length, we take the square root of both sides:
\[ \text{Side} = \sqrt{36 \, \text{cm}^2} = 6 \, \text{cm} \]

### Step 4: Calculate the Perimeter of the Square
The perimeter of a square is calculated using the formula:
\[ \text{Perimeter} = 4 \times \text{Side} \]
Substituting the side length we found:
\[ \text{Perimeter} = 4 \times 6 \, \text{cm} = 24 \, \text{cm} \]

### Final Answer
The perimeter of the square is \( 24 \, \text{cm} \).

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