Let's solve the problem step-by-step:
We are given:
- The perimeter of the rectangle is 24 cm.
- The length of the rectangle is double its breadth.
Let's denote the breadth of the rectangle by [tex]\( x \)[/tex] cm.
Since the length of the rectangle is double its breadth, the length will be [tex]\( 2x \)[/tex] cm.
Step-by-Step Solution:
### Step 1: Perimeter of the Rectangle
The formula to calculate the perimeter of a rectangle is:
[tex]\[ \text{Perimeter} = 2 \times (\text{length} + \text{breadth}) \][/tex]
Plugging in the given values:
[tex]\[ 24 = 2 \times (2x + x) \][/tex]
### Step 2: Solve for Breadth (x)
Simplify the equation:
[tex]\[ 24 = 2 \times (3x) \][/tex]
[tex]\[ 24 = 6x \][/tex]
Divide both sides by 6:
[tex]\[ x = \frac{24}{6} \][/tex]
[tex]\[ x = 4 \][/tex]
So, the breadth (x) is 4 cm.
### Step 3: Calculate the Length
Since the length is double the breadth:
[tex]\[ \text{Length} = 2 \times x \][/tex]
[tex]\[ \text{Length} = 2 \times 4 \][/tex]
[tex]\[ \text{Length} = 8 \][/tex]
So, the length is 8 cm.
### Step 4: Calculate the Area
The formula to calculate the area of a rectangle is:
[tex]\[ \text{Area} = \text{length} \times \text{breadth} \][/tex]
Substitute the values we found:
[tex]\[ \text{Area} = 8 \times 4 \][/tex]
[tex]\[ \text{Area} = 32 \][/tex]
So, the area of the rectangle is 32 square cm.
### Final Results:
i. Length: 8 cm
ii. Breadth: 4 cm
iii. Area: 32 square cm
