Question

A breeder of horses wants to fence two adjacent rectangular grazing areas along a river with 600meters of fence.

a. Write an expression for the total area, A, of the grazing land in terms of the width,
w, of the rectangle.

Answer 1

notice the picture below

the perimeter for both areas is w + w + w + l
since one part of the rectangle is covered by the river's edge

thus
`\bf \begin{cases} A=lw\\\\ P=3w+l\\\\ 600-3w=\boxed{l}\\ ----------\\ A=\left( \boxed{600-3w} \right)w \end{cases} \qquad \begin{array}{llll} A=\textit{area of a rectangle}\\ P=\textit{perimeter of a rectangle}\\ w=width\\ l=length \end{array}`