Answer
The perimeter $P$ of the rectangular floor as a function of the width $x$ is:
$P\left( x \right)=2x+\frac{5000}{x}$.
Work Step by Step
Consider the length of the rectangle to be y.
The width of the rectangular floor is $x$.
The area of the rectangular floor of the house is $2500$ square feet.
Substitute $A=2500$ in the formula $A=xy$.
$\begin{align}
& 2500=xy \\
& \frac{2500}{x}=y
\end{align}$
Substitute $y=\frac{2500}{x}$ in the formula $P=2x+2y$.
$\begin{align}
& P=2x+2\left( \frac{2500}{x} \right) \\
& =2x+\frac{5000}{x}
\end{align}$
Therefore, the perimeter $P$ of the rectangular floor as a function of the width $x$ is $P\left( x \right)=2x+\frac{5000}{x}$.
