Certainly! Let's go through the problem step-by-step.
### (i) Write the formula to find the perimeter of a rectangle.
The formula to find the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[ P = 2 \times (\text{length} + \text{breadth}) \][/tex]
### (ii) Find its breadth.
We are given:
- The length of the rectangle is 9 cm.
- The perimeter of the rectangle is 30 cm.
Using the perimeter formula:
[tex]\[ P = 2 \times (\text{length} + \text{breadth}) \][/tex]
Plugging in the given values:
[tex]\[ 30 = 2 \times (9 + \text{breadth}) \][/tex]
To find the breadth, we solve for the breadth step-by-step:
1. Divide both sides of the equation by 2:
[tex]\[ 15 = 9 + \text{breadth} \][/tex]
2. Subtract 9 from both sides:
[tex]\[ 15 - 9 = \text{breadth} \][/tex]
3. This gives us:
[tex]\[ \text{breadth} = 6 \text{ cm} \][/tex]
So, the breadth of the rectangle is 6 cm.
### (iii) Find its area.
The formula to find the area [tex]\( A \)[/tex] of a rectangle is:
[tex]\[ A = \text{length} \times \text{breadth} \][/tex]
Using the values we have:
- Length = 9 cm
- Breadth = 6 cm
Plugging these values into the area formula:
[tex]\[ A = 9 \times 6 = 54 \text{ cm}^2 \][/tex]
So, the area of the rectangle is 54 square centimeters.
