word problem

Question

A rancher has 400 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectangular plots by placing a fence parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.

Answer 1

3W + 2L = 400

A = 2*(W*L)

Rewrite the first equation so you can substitute it into the second. Rewrite into a quadratic equation. Replace the A with y and the W or L with x. Find the vertex (maximum) of the parabola. That will give you one dimension which you can use to find the second.