Answer
The expression for the area of the rectangular field in terms of one of the dimensions of the field x is \[A\left( x \right)=\frac{x\left( 1000-2x \right)}{3}\]
Work Step by Step
The amount of fencing required would be equal to the sum of the length of all the sides including the partition.
Write the equation for total fencing required to enclose the ground.
$2x+3y=1000$
Calculate $y$ in terms of x.
$\begin{align}
& 2x+3y=1000 \\
& 3y=1000-2x \\
& y=\frac{1000-2x}{3}
\end{align}$
Consider the area of the rectangular field.
$A=xy$
Substitute $\frac{1000-2x}{3}$ for y.
$A=x\left( \frac{1000-2x}{3} \right)$
Because A is a function of x, it can be written as,
$\begin{align}
& A\left( x \right)=x\left( \frac{1000-2x}{3} \right) \\
& =\frac{x\left( 1000-2x \right)}{3}
\end{align}$
Hence, the expression for the area of the rectangular field in terms of one of the dimensions of the field x is $A\left( x \right)=\frac{x\left( 1000-2x \right)}{3}$
