Answer
The expression for the area of the rectangular field in terms of one of the dimensions of the field x is $A\left( x \right)=-{{x}^{2}}+300x$.
Work Step by Step
Let the 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.
$2x+2y=600$
Calculate $y$ in terms of x.
$\begin{align}
& 2y=600-2x \\
& y=\frac{600-2x}{2} \\
& y=300-x
\end{align}$
Consider the area of the rectangular field.
$A=xy$
Substitute $300-x$ for y.
$A=x\left( 300-x \right)$
Because A is a function of x, it can be written as,
$\begin{align}
& A\left( x \right)=x\left( 300-x \right) \\
& =300x-{{x}^{2}} \\
& =-{{x}^{2}}+300x
\end{align}$
Hence, the expression for the area of the rectangular field in terms of one of the dimensions of the field x is $A\left( x \right)=-{{x}^{2}}+300x$.
