Question 1044598
Let {{{ s }}} = the length of one of  the sides which
is perpendicular to the river
{{{ 2400 - 2s }}} = the length of the side which 
is parallel to the river
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Let {{{ A }}} = the area of the rectangular field in square ft
{{{ A = s*( 2400 - 2s ) }}}
{{{ A = -2s^2 + 2400s }}}
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If the form of the equation looks like:
{{{ f(s) = a*s^2 + b*s + c }}}, then the s-value of the
vertex of the parabola is:
{{{ s[v] = -b/(2a) }}}
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In this case:
{{{ a = -2 }}}
{{{ b = 2400 }}}
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{{{ s[v] = ( -2400 ) / ( 2*(-2) ) }}}
{{{ s[v] = 600 }}}
and
{{{ A[v] = s*( 2400 - 2s ) }}}
{{{ A[v] = 600*( 2400 - 1200 ) }}}
{{{ A[v] = 600*1200 }}}
{{{ A[v] = 720000 }}}
The maximum area is 720,000 ft2
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Knowing this, you can try a slightly different 
shape for the rectangular field, say by making
{{{ s = 598 }}}
{{{ 2400 - 2s = 2400 - 1196 }}}
{{{ 2400 - 2s = 1204 }}}
{{{ A = 598*1204 }}}
{{{ A = 719992 }}}
This is clearly a little less than the maximum area
I just got
Now try:
{{{ s = 602 }}}
{{{ 2400 - 2s = 2400 - 1204 }}}
{{{ 2400 - 2s = 1196 }}}
{{{ A = 602*1196 }}}
{{{ A = 719992 }}}
Also a little less than maximum area ( same number as before )
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Here's a plot of the equation for area:
{{{ graph( 600, 400, -250, 1500, -80000, 800000, -2x^2 + 2400x ) }}}