Question

The difference between Length and breadth is 2, total land area is 5.04 lakh at the rate of 3000 m². Find the largest perimeter.

Hint:

In problems involving rectangles, use the area and the relationship between length and breadth to find the dimensions and then calculate the perimeter.

Answer 1

Step 1: Let the dimensions be L and B.
Let the length of the rectangle be \( L \) and the breadth be \( B \). We are given that \( L = B + 2 \). The area of the rectangle is: \[ L \times B = 5.04 \times 10^5 \, \text{m}^2 \]
Step 2: Express the area.
Substitute \( L = B + 2 \) into the area formula: \[ (B + 2) \times B = 5.04 \times 10^5 \]
Step 3: Solve for B.
Expanding the equation: \[ B^2 + 2B = 5.04 \times 10^5 \] Solving this quadratic equation gives: \[ B = 250 \]
Step 4: Find L.
Now, substitute \( B = 250 \) into \( L = B + 2 \): \[ L = 252 \]
Step 5: Calculate the perimeter.
The perimeter of the rectangle is: \[ \text{Perimeter} = 2(L + B) = 2(252 + 250) = 2 \times 502 = 52 \, \text{meters} \]