The diagonal of a rectangular field is 15 metres and the difference between its length its length and width is 3 metres. The area of the rectangular field is :

Answer: Option D

Let l and b be the length and breadth of the rectangle respectively.
Then,
$$\begin{array}{rl}& \Rightarrow \sqrt{l^2+b^2}=15\\ & \Rightarrow \left(l^2+b^2\right)={\left(15\right)}^2\\ & \Rightarrow l^2+b^2=225\end{array}$$
And,
$$\begin{array}{rl}& \Rightarrow l+b=3\\ & \\ & \Rightarrow {\left(l-b\right)}^2=9\\ & \Rightarrow l^2+b^2-2lb=9\\ & \Rightarrow 225-2lb=9\\ & \Rightarrow 2lb=216\\ & \Rightarrow lb=108\end{array}$$
Hence, area of the field $$=lb=108m^2$$