This worksheet looks at the classic optimization problem of finding the maximum area enclosed by a fence given a certain amount of fence to work with. There are two problems: one asks for the maximum area of a rectangular fence and the other asks for the same thing when the fence is placed with one side along a river. Both problems result in the student solving a quadratic.
The first problem is explored in detail with guidance for the student. The second problem allows the student to solve the problem mostly on their own.
This is appropriate for Algebra 1, Algebra 2, or Precalculus. Calculus is not used to arrive at the answers.
A detailed answer key is provided.