The perimeter of a rectangular plot of land is 80 m and its breadth is 16 m . Find the length and area of the plot .

Answer

To solve the problem step by step, we will follow the given information about the rectangular plot of land.

### Step 1: Understand the formula for the perimeter of a rectangle.
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (L + B) \]
where \( L \) is the length and \( B \) is the breadth.

### Step 2: Substitute the known values into the perimeter formula.
We know the perimeter \( P = 80 \, \text{m} \) and the breadth \( B = 16 \, \text{m} \). We can substitute these values into the formula:
\[ 80 = 2 \times (L + 16) \]

### Step 3: Simplify the equation.
To simplify, divide both sides of the equation by 2:
\[ 40 = L + 16 \]

### Step 4: Solve for the length \( L \).
Now, we can isolate \( L \) by subtracting 16 from both sides:
\[ L = 40 - 16 \]
\[ L = 24 \, \text{m} \]

### Step 5: Calculate the area of the rectangle.
The area \( A \) of a rectangle is calculated using the formula:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 24 \times 16 \]

### Step 6: Perform the multiplication to find the area.
Calculating the area:
\[ A = 384 \, \text{m}^2 \]

### Final Answers:
- Length of the plot: \( 24 \, \text{m} \)
- Area of the plot: \( 384 \, \text{m}^2 \)

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