The permeter of a rectangle is 40 cm. The length of the rectangle is more than double its breadth by 2. Find length and breadth.

Answer

To solve the problem step by step, we will define the variables, set up equations based on the given information, and then solve for the length and breadth of the rectangle.

### Step 1: Define the Variables
Let:
- \( L \) = Length of the rectangle
- \( B \) = Breadth of the rectangle

### Step 2: Set Up the Equations
1. The perimeter of a rectangle is given by the formula:
\[ \text{Perimeter} = 2(L + B) \]
According to the problem, the perimeter is 40 cm. Therefore, we can write:
\[ 2(L + B) = 40 \]
Dividing both sides by 2 gives us:
\[ L + B = 20 \quad \text{(Equation 1)} \]

2. The problem states that the length is more than double its breadth by 2. This can be expressed as:
\[ L = 2B + 2 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1
Now, we will substitute Equation 2 into Equation 1:
\[ (2B + 2) + B = 20 \]
Combining like terms:
\[ 3B + 2 = 20 \]

### Step 4: Solve for Breadth \( B \)
Subtract 2 from both sides:
\[ 3B = 20 - 2 \]
\[ 3B = 18 \]
Now, divide both sides by 3:
\[ B = \frac{18}{3} = 6 \text{ cm} \]

### Step 5: Solve for Length \( L \)
Now that we have the breadth, we can find the length using Equation 2:
\[ L = 2B + 2 \]
Substituting \( B = 6 \):
\[ L = 2(6) + 2 = 12 + 2 = 14 \text{ cm} \]

### Final Answer
The length of the rectangle is \( 14 \) cm and the breadth is \( 6 \) cm.