The breadth of a rectangular field is 3/4 of its length and its area is 300 sq. metres. What will be the area (in sq. metres) of the garden of breath 1.5 metres developed around the field ?

Answer: Option C

Let the length of the field be x metres
Then, breadth of the field = $$\frac{3x}{4}$$ metres
$$\begin{array}{rl}& x\times \frac{3x}{4}=300\\ & \Rightarrow x^2=300\times \frac{4}{3}\\ & \Rightarrow x^2=400\\ & \Rightarrow x=20\end{array}$$
So, length = 20 m, breadth = 15 m
∴ Area of the garden :
$$\begin{array}{rl}& =\left[\left\{\left(20+3\right)\times \left(15+3\right)\right\}-\left(20\times 15\right)\right]m^2\\ & =\left[\left(23\times 18\right)-\left(20\times 15\right)\right]m^2\\ & =\left(414-300\right)m^2\\ & =114m^2\end{array}$$