The perimeter of a rectangular plot of land is 240 m and its length is 63 m . Find the breadth and area of the plot.

Answer

To solve the problem step by step, we will use the given information about the perimeter and length of the rectangular plot.

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

### Step 2: Substitute the known values into the perimeter formula.
We know the perimeter is 240 m and the length is 63 m. So we can substitute these values into the formula:
\[ 240 = 2(63 + B) \]

### Step 3: Simplify the equation.
To simplify, divide both sides of the equation by 2:
\[ 120 = 63 + B \]

### Step 4: Solve for the breadth (B).
Now, isolate \( B \) by subtracting 63 from both sides:
\[ B = 120 - 63 \]
\[ B = 57 \text{ m} \]

### Step 5: Calculate the area of the rectangle.
The area (A) of a rectangle is given by the formula:
\[ A = L \times B \]
Substituting the values we have:
\[ A = 63 \times 57 \]

### Step 6: Perform the multiplication to find the area.
Calculating the area:
\[ A = 63 \times 57 = 3591 \text{ m}^2 \]

### Final Answer:
- The breadth of the rectangular plot is **57 m**.
- The area of the rectangular plot is **3591 m²**.

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