Thread: Quadratic Story Problem

Question:
A Building contractor wants to fence in a rectangular plot adjacent to a strait highway using the highway for one side, which will be left unfenced. If the contractor has 500 ft of fence , find the dimensions of the maximum enclosed area.

I know the answer to this question is 125x250, but I have no idea how they got that. It doesn't seem like there is enough information without assuming that the rectangle's sides are A x 2A x A x 2A(the last side not fenced). Should I be assuming this? How should I set up this problem?

A rectangular plot need not have A x 2A x A x 2A

You know the perimeter = 500 and that area = MAX

so,
2a + b = 500
and
ab = MAX

use substitution and you get a quadratic where the MAX is the value at the vertex of the downward parabola.