The length of a rectangle is ` 6//5^(th)` of its breadth. If the perimeter is 132 m, its area will be

Options

A. `640 m^(2)`
B. ` 1,080 m^(2)`
C. ` 1,620 m^(2)`
D. ` 2,160 m^(2)`

Answer

To solve the problem step by step, we will follow the given information about the rectangle's dimensions and its perimeter.

### Step 1: Define Variables
Let the breadth of the rectangle be \( B \) meters. According to the problem, the length \( L \) is given as:
\[ L = \frac{6}{5}B \]

### Step 2: Write the Perimeter Formula
The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2(L + B) \]
We know the perimeter is 132 meters, so we can set up the equation:
\[ 2(L + B) = 132 \]

### Step 3: Substitute the Length in the Perimeter Equation
Substituting \( L \) from Step 1 into the perimeter equation:
\[ 2\left(\frac{6}{5}B + B\right) = 132 \]

### Step 4: Simplify the Equation
Combine the terms inside the parentheses:
\[ 2\left(\frac{6}{5}B + \frac{5}{5}B\right) = 132 \]
\[ 2\left(\frac{11}{5}B\right) = 132 \]

### Step 5: Solve for Breadth \( B \)
Now, simplify the equation:
\[ \frac{22}{5}B = 132 \]
Multiply both sides by \( \frac{5}{22} \):
\[ B = 132 \times \frac{5}{22} \]
Calculating this gives:
\[ B = 30 \text{ meters} \]

### Step 6: Calculate Length \( L \)
Now, substitute \( B \) back to find \( L \):
\[ L = \frac{6}{5}B = \frac{6}{5} \times 30 = 36 \text{ meters} \]

### Step 7: Calculate the Area
The area \( A \) of the rectangle is given by:
\[ A = L \times B \]
Substituting the values of \( L \) and \( B \):
\[ A = 36 \times 30 = 1080 \text{ square meters} \]

### Final Answer
The area of the rectangle is \( 1080 \) square meters.

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