#### Answer

The area, A of the rectangle $A=xy$.
The perimeter, P of rectangle is $P=2x+2y$. If the perimeter of the rectangle is $180\ \text{inches}$, then $y=90-x$. Substituting this formula for y in the expression of area, the area of a rectangle can be expressed as $A\left( x \right)=x\left( 90-x \right)$.

#### Work Step by Step

Consider the length and breadth of the rectangle
Length is x, breadth is y.
$\begin{align}
& \text{Area of rectangle}=L\cdot B \\
& \text{Perimeter of rectangle}=2\left( L+B \right)
\end{align}$
Where L, B are the length and breadth of the rectangle.
Now,
$\begin{align}
& \text{Area of rectangle}=L\cdot B \\
& =x\cdot y \\
& =xy
\end{align}$
And
$\begin{align}
& \text{Perimeter of rectangle}=2\left( L+B \right) \\
& =2\left( x+y \right) \\
& =2x+2y
\end{align}$
Now, the perimeter of the rectangle is $180\ \text{inches}$.
From here,
$2x+2y=180$
Divide both sides by 2
$\left( x+y \right)=90$
From here,
$y=90-x$
Now, the area of the rectangle is given by:
$\begin{align}
& \text{Area of rectangle}=x\cdot y \\
& =x\left( 90-x \right)
\end{align}$