Question

The dimensions of a rectangular park are \(75\text{ m} \times 55\text{ m}\). A walking path of breadth \(2.5\) m is laid on the outside and along the boundary of the park. The area of the path in sq. meters is:

• A. \(1125\)
• B. \(1000\)
• C. \(875\)
• D. \(675\)

Hint:

Whenever a path surrounds a rectangle externally, increase both dimensions by twice the width of the path before calculating the outer area.

Answer 1

The Correct Option is A

Concept: Area of path \[ = \text{Area of outer rectangle} - \text{Area of park} \]

Step 1: Find the dimensions of the outer rectangle. Breadth of path: \[ 2.5\text{ m} \] Since the path is outside all around, \[ \text{New length} = 75+2(2.5) = 80 \] \[ \text{New breadth} = 55+2(2.5) = 60 \]

Step 2: Calculate the outer area. \[ 80\times60 = 4800 \] sq. m.

Step 3: Calculate the area of the park. \[ 75\times55 = 4125 \] sq. m.

Step 4: Find the area of the path. \[ 4800-4125 = 675 \] sq. m. Therefore, \[ \boxed{675} \] Note: The mathematical calculation gives \(675\) sq. m. Hence option (D) is correct though some keys may vary.