The perimeter of rectangle whose length is 6m more than its breadth is 84m what will be area of rectangle

Options

A. 446
B. 340
C. 432
D. 468

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let the breadth of the rectangle be \( x \) meters. According to the problem, the length of the rectangle is 6 meters more than its breadth. Therefore, we can express the length as:
\[ \text{Length} = x + 6 \text{ meters} \]

### Step 2: Write the Perimeter Formula
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]
Substituting the expressions for length and breadth, we have:
\[ P = 2 \times ((x + 6) + x) \]

### Step 3: Substitute the Given Perimeter
We know from the problem that the perimeter is 84 meters. Therefore, we can set up the equation:
\[ 84 = 2 \times ((x + 6) + x) \]

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ 84 = 2 \times (2x + 6) \]
Dividing both sides by 2 gives:
\[ 42 = 2x + 6 \]

### Step 5: Solve for \( x \)
Next, we isolate \( x \) by subtracting 6 from both sides:
\[ 42 - 6 = 2x \]
\[ 36 = 2x \]
Now, divide both sides by 2:
\[ x = 18 \]

### Step 6: Find the Length
Now that we have the breadth, we can find the length:
\[ \text{Length} = x + 6 = 18 + 6 = 24 \text{ meters} \]

### Step 7: Calculate the Area
The area \( A \) of the rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Substituting the values we found:
\[ A = 24 \times 18 \]

### Step 8: Perform the Multiplication
Now, calculate the area:
\[ A = 432 \text{ square meters} \]

### Conclusion
The area of the rectangle is \( 432 \) square meters.

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