Math
posted by Taylor on .
A farmer needs to enclose three sides of a pasture with a fence (the fourth side is a river). The farmer has 42 meters of fence and wants the pasture to have an area of 220 sqmeters. What should the dimensions of the pasture be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.)

If the width is w, then the length is 422w. So, the area is
y = w(422w)
y = 2w^2 + 42w
this is just a parabola, and y reaches its maximum when w = 42/4 = 10.5
so, the pasture is 10.5 x 21. Area = 220.5
If we want just 220 m^2, then the field is 11x20