Answer
The expression of cost to enclose the rectangular garden in terms of one of the dimensions $x$ is $C\left( x \right)=29x+\frac{5000}{x}$.
Work Step by Step
Let the length of the garden be x and breadth of the garden be $y$.
Write the expression for the area of the rectangular garden.
$xy=125$
Calculate y in terms of x.
$y=\frac{125}{x}$
Write the expression for the cost of building three brick walls around the garden which costs $\$20\text{perfoot}$ and fencing around one side which costs $\$9\text{perfoot}$
$C=20\left( x+2y \right)+9x$
Substitute $\frac{125}{x}$ for $y$.
$\begin{align}
& C=20\left[ x+2\left( \frac{125}{x} \right) \right]+9x \\
& =20x+\frac{5000}{x}+9x \\
& =29x+\frac{5000}{x}
\end{align}$
The cost is function of x, so it can be expressed as,
$C\left( x \right)=29x+\frac{5000}{x}$
Hence, expression of cost to enclose the rectangular garden in terms of one of the dimensions $x$ is $C\left( x \right)=29x+\frac{5000}{x}$.
