## Precalculus (6th Edition) Blitzer

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 $A\left( x \right)=x\left( 90-x \right)$.
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}