OFFICIAL EXPLANATION

Let the length \& the breadth of the small rectangular park be L \& B respectively.

As the perimeter of the rectangular park is 560 feet, we get $$2(L+B)=560 \Rightarrow L+B=280$$

Also as the diagonal of the park is 200 feet, we get $$L^2+B^2=200^2=40000$$ where

$$\(\begin\mathrm{L}^2+\mathrm{B}^2=(\mathrm{L}+\mathrm{B})^2-2 \mathrm{LB}=(280)^2-2 \mathrm{LB}=78400-2 \mathrm{LB} \\ \)$$

which gives

$78400-2 \mathrm{LB}=40000 \Rightarrow \mathrm{LB}=\frac{38400}{2}=19200$

Hence the answer is (A).