Question

A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. find the dimensions of the land that require the least amount of fencing.

Answer 1

Let x = the length of the rectangle
Let w= the width

Two sections are required, hence 2w of fence required
2x+3w=500

this can be written as:
3w=1500-2x
w=(1500-2x)/3

Area=x*w
replacing w with our expression:
A=x(1500-2x)/3
A=(500x-2x^2)/3

This is a quadratic equation, if we find the axis of symmetry we will know what value of x gives maximum area:
Axis of symmetry: x=-b/2a
From our equation we get:
a=-2/3; b=1500/3
thus
x=(1500/3)/(-(-2/3))
x=750
thus the maximum area will be given by length of 750