The perimeter of a rectangular field is 216 metres and its breadth is 40 metres . Find the length and area of the rectangle.

Options

A. `=4720 m^(2)`.
B. `=3720 m^(2)`.
C. `=2920 m^(2)`.
D. `=2720 m^(2)`.

Answer

To solve the problem step by step, we will follow the process of finding the length and area of the rectangle given the perimeter and breadth.

### Step 1: Understand the formula for the perimeter of a rectangle.
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2 \times ( \text{Length} + \text{Breadth} ) \]

### Step 2: Substitute the known values into the formula.
We know that the perimeter is 216 meters and the breadth is 40 meters. We can substitute these values into the formula:
\[ 216 = 2 \times ( \text{Length} + 40 ) \]

### Step 3: Simplify the equation.
First, we can divide both sides of the equation by 2 to simplify:
\[ 108 = \text{Length} + 40 \]

### Step 4: Solve for the length.
Now, we can isolate the length by subtracting 40 from both sides:
\[ \text{Length} = 108 - 40 \]
\[ \text{Length} = 68 \text{ meters} \]

### Step 5: Calculate the area of the rectangle.
The area (A) of a rectangle can be calculated using the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Substituting the values we found:
\[ A = 68 \times 40 \]

### Step 6: Perform the multiplication to find the area.
\[ A = 2720 \text{ square meters} \]

### Final Answer:
- Length of the rectangle: 68 meters
- Area of the rectangle: 2720 square meters

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