## Precalculus (6th Edition) Blitzer

The expression for the area of a rectangular field in terms of one of the dimension of the field x is $A\left( x \right)=-{{x}^{2}}+400x$.
Let length of the field be $x$ and breadth of the field be $y$. Consider the perimeter of the rectangular field which will equal to the fencing required to enclose the field. 2x+2y=800 Calculate $y$ in terms of x. \begin{align} & 2y=800-2x \\ & y=\frac{800-2x}{2} \\ & y=400-x \end{align} Consider the area of the rectangular field. $A=xy$ Substitute $400-x$ for y. $A=x\left( 400-x \right)$ Because A is a function of x, it can be written as, \begin{align} & A\left( x \right)=x\left( 400-x \right) \\ & =400x-{{x}^{2}} \\ & =-{{x}^{2}}+400x \end{align} Hence, the expression for the area of the rectangular field in terms of one of the dimension of the field x is $A\left( x \right)=-{{x}^{2}}+400x$.