Question 1023610
Perimeter of the fence,
{{{L+2W=100}}}
Area enclosed by fence,
{{{A=L*W}}}
Substituting,
{{{A=(100-2W)W}}}
{{{A=100W-2W^2}}}
Converting to vertex form,
{{{A=-2W^2+100W}}}
{{{A=-2(W^2-50W)}}}
{{{A=-2(W^2-50W+625)+2(625)}}}
{{{A=-2(W-25)^2+1250}}}
So now in vertex form, the vertex is the maximum (since the quadratic multiplier ({{{-2}}}) is negative).
The maximum area occurs at {{{W=25}}}{{{m}}} and is equal to {{{A[max]=1250}}}{{{m^2}}}
{{{L=100-2(25)}}}
{{{L=100-50}}}
{{{L=50}}} {{{m}}}