A rectangle has perimeter 132 cm. Its length is 9 cm more than twice its breadth . Find its area.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given information
We know that the perimeter of the rectangle is 132 cm and that the length (L) is 9 cm more than twice the breadth (B).

### Step 2: Write the formula for the perimeter of a rectangle
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2(L + B) \]
Given that the perimeter is 132 cm, we can set up the equation:
\[ 2(L + B) = 132 \]

### Step 3: Simplify the perimeter equation
Dividing both sides of the equation by 2 gives:
\[ L + B = 66 \]

### Step 4: Express the length in terms of breadth
From the problem, we know that:
\[ L = 2B + 9 \]
Now we can substitute this expression for L into the equation we derived from the perimeter.

### Step 5: Substitute and solve for breadth
Substituting \( L \) in the perimeter equation:
\[ (2B + 9) + B = 66 \]
Combining like terms:
\[ 3B + 9 = 66 \]
Now, subtract 9 from both sides:
\[ 3B = 57 \]
Dividing both sides by 3 gives:
\[ B = 19 \]

### Step 6: Find the length
Now that we have the breadth, we can find the length using the expression we derived:
\[ L = 2B + 9 \]
Substituting \( B = 19 \):
\[ L = 2(19) + 9 = 38 + 9 = 47 \]

### Step 7: Calculate the area of the rectangle
The area (A) of a rectangle is given by:
\[ A = L \times B \]
Substituting the values of L and B:
\[ A = 47 \times 19 \]

### Step 8: Perform the multiplication
Calculating the area:
\[ A = 893 \, \text{cm}^2 \]

### Final Answer
The area of the rectangle is \( 893 \, \text{cm}^2 \).

---