Answer
The expression for the area of the rectangular field in terms of one of the dimensions of the field x is \[A\left( x \right)=-2{{x}^{2}}+800x\]
Work Step by Step
Let the length of the field be $x$ and breadth of the field be $y$.
The amount of fencing required will be equal to the sum of twice x and y.
$2x+y=800$
Calculate $y$ in terms of x.
$y=800-2x$
Consider the area of the rectangular field.
$A=xy$
Substitute $800-2x$ for y.
$A=x\left( 800-2x \right)$
Because A is a function of x, it can be written as,
$\begin{align}
& A\left( x \right)=x\left( 800-2x \right) \\
& =800x-2{{x}^{2}} \\
& =-2{{x}^{2}}+800x
\end{align}$
Hence, the expression for the area of the rectangular field in terms of one of the dimensions of the field x is $A\left( x \right)=-2{{x}^{2}}+800x$.
