Question 593762
Start with:
{{{P = 2(L+W)}}} Substitute P = 168.
{{{168 = 2(L+W)}}} Divide both sides by 2.
{{{84 = L+W}}} Rewrite as:
{{{L = 84-W}}} and substitute into;
{{{A = L*W}}}
{{{A = (84-W)*W}}}  Simplify.
{{{A = 84W-W^2}}} Rewrite this as:
{{{-W^2+84W-A = 0}}} This is a quadratic equation which yields a parabola opening downward when graphed. This is the graph of the area (vertical) versus the width (W) (horizontal).  The maximum point (W) on this graph, also known as the vertex, is given by:
{{{W = -b/2a}}} and a = -1, b = 84.
{{{W = -(84)/2(-1)}}}
{{{W = 42}}}
The dimensions for the maximum area will 42 by 42 which is a square.