To solve the problem step by step, we need to find the area of the rectangle, determine the side of the square, calculate the perimeter of both figures, and then compare them.
### Step 1: Calculate the area of the rectangle
The formula for the area of a rectangle is:
\[
\text{Area} = \text{Length} \times \text{Breadth}
\]
Given:
- Length = 9 cm
- Breadth = 4 cm
So, the area of the rectangle is:
\[
\text{Area} = 9 \, \text{cm} \times 4 \, \text{cm} = 36 \, \text{cm}^2
\]
### Step 2: Determine the side of the square
Since the area of the square is the same as the area of the rectangle, we have:
\[
\text{Area of square} = 36 \, \text{cm}^2
\]
The formula for the area of a square is:
\[
\text{Area} = \text{Side} \times \text{Side} = \text{Side}^2
\]
Thus, we can set up the equation:
\[
\text{Side}^2 = 36
\]
Taking the square root of both sides, we find:
\[
\text{Side} = 6 \, \text{cm
\]
### Step 3: Calculate the perimeter of the rectangle
The formula for the perimeter of a rectangle is:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})
\]
Substituting the values:
\[
\text{Perimeter} = 2 \times (9 \, \text{cm} + 4 \, \text{cm}) = 2 \times 13 \, \text{cm} = 26 \, \text{cm}
\]
### Step 4: Calculate the perimeter of the square
The formula for the perimeter of a square is:
\[
\text{Perimeter} = 4 \times \text{Side}
\]
Substituting the value of the side:
\[
\text{Perimeter} = 4 \times 6 \, \text{cm} = 24 \, \text{cm}
\]
### Step 5: Compare the perimeters
Now we compare the perimeters of the rectangle and the square:
- Perimeter of rectangle = 26 cm
- Perimeter of square = 24 cm
To find out which figure has the greater perimeter and by how much:
\[
\text{Difference} = \text{Perimeter of rectangle} - \text{Perimeter of square} = 26 \, \text{cm} - 24 \, \text{cm} = 2 \, \text{cm}
\]
### Final Answer
The perimeter of the rectangle is greater than the perimeter of the square by 2 cm.
---
