Answer
$\text{Length = 775 meters and Width = 725 meters}$
Work Step by Step
Let us consider that $x$=width (in meters) and $y$=length ( in meters).
We are given:
$y-x=50~~~(1) $
and the perimeter is:
$2x+2y=3000~~~(2)$
Re-write equation (1) as: $y=x+50 ~~~(3)$
Plug equation (3) into equation (2) to solve for $x$; then we get:
$2x+(2)(x+50)=3000 \\ 2x+2x+100=3000 \implies x=725$
Now, back substitute the value of $x$ into Equation (3) to solve for $y$:
$y=725+50 \implies y=775$
Therefore, the dimensions of the field are:
$\text{Length = 775 meters and Width = 725 meters}$
