A farmer has 1500 feet of fencing in his barn. He wishes to enclose a rectangular pen. Subdivided into two regions by a section of fence down the middle, parallel to one side of the rectangle. Express the area enclosed by the pen as a function of its width x.

Question

A farmer has 1500 feet of fencing in his barn.  He wishes to enclose a rectangular pen.  Subdivided  into two regions by a section of fence down the middle,  parallel to one side of the rectangle.  Express  the area enclosed by the pen as a function  of its width  x.

oobleck · Answer

So you have 2 long sections (x) and 3 short sections (y). 3x+2y = 1500 The area is A = xy = x(1500-3x)/2

oobleck · Answer

or, 2x+3y = 1500 whichever way you define width