The width of the path around a square field is 4.5m and its area is 105.75m2. Find the cost of fencing the path at the rate of Rs100 per meter.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. Rs 550
The width of the path around a square field = 4.5 m
The area of the path = 105.75 m2
The perimeter of a square = 4 × Side
The area of a square = (Side)2
Let each side of the field be x.
Each side with the path = x + 4.5 + 4.5 = x + 9
(x + 9)2 - x2 = 105.75
x2 + 18x + 81 - x2 = 105.75
18x + 81 = 105.75
18x = 105.75 - 81 = 24.75
x = 24.75/18 = 11/8
Each side of the square field = 11/8 m
Perimeter = 4(11/8) = 11/2 m
So, the total cost of fencing = 11/2(100) = Rs. 550