The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the path at the rate of Rs. 100 per metre.

Answer: Option A

Let the length of interior square = $$x$$
The length of exterior square = ($$x$$ + 9)
According to question
$$\begin{array}{rl}& {\left(x+9\right)}^2-x^2=105.75\\ & \left(x+9+x\right)\left(x+9-x\right)=\frac{10575}{100}\\ & \left(2x+9\right)\times 9=\frac{423}{4}\\ & 2x+9=\frac{47}{4}\\ & 2x=\frac{47}{4}-9\\ & 2x=\frac{11}{4}\\ & x=\frac{11}{8}\\ & \text{Total cost of fencing}\\ & =\frac{11}{8}\times 4\times 100\\ & =\text{Rs}\text{. }550\end{array}$$