The length of a rectangle is 2 cm more than its breadth. If the perimeter of the rectangle is 36 cm , find its length.

Answer

To find the length of the rectangle given that its length is 2 cm more than its breadth and the perimeter is 36 cm, we can follow these steps:

### Step 1: Define the variables
Let the breadth of the rectangle be denoted as \( b \) cm. According to the problem, the length \( L \) can be expressed as:
\[ L = b + 2 \]

### Step 2: Write the formula for the perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (L + b) \]
We know that the perimeter is 36 cm, so we can set up the equation:
\[ 2 \times (L + b) = 36 \]

### Step 3: Substitute the expression for length
Now, substitute \( L \) from Step 1 into the perimeter equation:
\[ 2 \times ((b + 2) + b) = 36 \]

### Step 4: Simplify the equation
Simplifying the left side, we get:
\[ 2 \times (2b + 2) = 36 \]
This simplifies to:
\[ 4b + 4 = 36 \]

### Step 5: Solve for breadth
Now, subtract 4 from both sides:
\[ 4b = 36 - 4 \]
\[ 4b = 32 \]
Now, divide both sides by 4:
\[ b = \frac{32}{4} \]
\[ b = 8 \text{ cm} \]

### Step 6: Find the length
Now that we have the breadth, we can find the length using the expression from Step 1:
\[ L = b + 2 \]
Substituting the value of \( b \):
\[ L = 8 + 2 \]
\[ L = 10 \text{ cm} \]

### Final Answer
The length of the rectangle is \( 10 \) cm.

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