Question 59545
If the side parallel to the river is x, 
the remaining 2 sides are equal and each
equals {{{(3000 - x)/2}}}
{{{A = x*(3000 - x) / 2}}}
{{{A = -(1/2)x^2 + 1500x}}}
{{{ graph( 700, 500, -300, 3200, -50000, 1200000, -(1/2)*x^2 + 1500x) }}}
From the graph, it looks like A is maximum when x = 1500
A would be (1500)^2 / 2 then or 1,125,000 sqare feet
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{{{C = x}}} answer
to find the area in terms of x, first find the area in terms of the 
circumference
{{{A = pi*r^2}}} where r is the radius
{{{C = 2*pi*r}}}
{{{C = x}}} ,so
{{{x = 2*pi*r}}}
Another way to express A is
{{{A = pi*r*r}}}
multiply both sides by 2
{{{2A = 2*pi*r*r}}}
{{{2A = x*r}}}
but
{{{r = x / (2*pi)}}}
so
{{{2A = x*(x / (2*pi))}}}
{{{A = x^2 / (4*pi)}}} answer