#### Answer

The expression for the area of a rectangular field in terms of one of the dimension of the field x is \[A\left( x \right)=-{{x}^{2}}+400x\].

#### Work Step by Step

Let length of the field be $x$ and breadth of the field be $y$.
Consider the perimeter of the rectangular field which will equal to the fencing required to enclose the field.
2x+2y=800
Calculate $y$ in terms of x.
$\begin{align}
& 2y=800-2x \\
& y=\frac{800-2x}{2} \\
& y=400-x
\end{align}$
Consider the area of the rectangular field.
$A=xy$
Substitute $400-x$ for y.
$A=x\left( 400-x \right)$
Because A is a function of x, it can be written as,
$\begin{align}
& A\left( x \right)=x\left( 400-x \right) \\
& =400x-{{x}^{2}} \\
& =-{{x}^{2}}+400x
\end{align}$
Hence, the expression for the area of the rectangular field in terms of one of the dimension of the field x is $A\left( x \right)=-{{x}^{2}}+400x$.