Question

The area of the rectangular park whose length is 7 meters more than its breadth is 260 sq meters. For fencing the entire boundary of the park if ₹9000 is spent, then the cost of fencing per meter is (in ₹):

• A. 165
• B. 160
• C. 136
• D. 155

Hint:

In problems involving area and perimeter of rectangles, always use the quadratic formula when setting up the equations for length and breadth.

Answer 1

The Correct Option is C

Let the breadth of the park be \( x \) meters. Then the length of the park is \( x + 7 \) meters. The area of the rectangular park is given as 260 sq meters: \[ \text{Area} = \text{Length} \times \text{Breadth} = (x + 7) \times x = 260 \] Expanding and solving for \( x \): \[ x^2 + 7x = 260 \] \[ x^2 + 7x - 260 = 0 \] Solving this quadratic equation using the quadratic formula: \[ x = \frac{-7 \pm \sqrt{7^2 - 4(1)(-260)}}{2(1)} = \frac{-7 \pm \sqrt{49 + 1040}}{2} = \frac{-7 \pm \sqrt{1089}}{2} = \frac{-7 \pm 33}{2} \] Thus, \( x = \frac{-7 + 33}{2} = 13 \) or \( x = \frac{-7 - 33}{2} = -20 \) (discarding the negative value as the breadth cannot be negative). So, the breadth is 13 meters, and the length is \( 13 + 7 = 20 \) meters. Step 1: The perimeter of the park is: \[ \text{Perimeter} = 2 \times (\text{Length} + \text{Breadth}) = 2 \times (20 + 13) = 66 \text{ meters} \]

Step 2: The total cost of fencing is ₹9000, so the cost per meter is: \[ \text{Cost per meter} = \frac{9000}{66} = 136.36 \]