The ratio of length to breadth of a rectangular field $8:6$ . If its diagonal is 200 m, then the area of the field in square meters is

Let the length and breadth of a rectangle be $8x$ and $6x$

In $\Delta ABC,A{C}^2={\left(8x\right)}^2+{\left(6x\right)}^2$

$=100x^2$

$AC=10x$

Since $10x=200\Rightarrow x=20$

Length $l=8\left(20\right)=160\text{m}$

Breadth $b=6\left(20\right)=120\text{m}$

Area of the field $=lb=160\times 120$

$=19,200m^2$