Question 378626
The optimum area of a rectangle with a given perimeter is a square, i.e in this case, the side length would be 17 feet and the area would be 289 ft^2.

However, proving this requires some introductory calculus.

If we define a function {{{A(x) = x(34-x) = 34x - x^2}}} then to optimize the value of A(x), we find A'(x) (the derivative of A(x) in terms of x).

By the power rule, A'(x) = 34 - 2x. The function reaches a critical point, or vertex, when A'(x) = 0, or x = 17. It can be verified that values greater or less than 17 will give smaller areas, so x = 17 is the optimum value.