Question 1087313
Let {{{ L }}} = the length parallel to the river
Let {{{ W }}} = the width of the other 2 sides
Let {{{ A }}} = the area of the rectangular plot
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{{{ 98 = L + 2W }}}
{{{ L = 98 - 2W }}}
{{{ A = L*W }}}
{{{ A = ( 98 - 2W )*W }}}
{{{ A = -2W^2 + 98W }}}
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The formula for {{{ W[max] }}} is:
{{{ W[max] = -b/( 2a ) }}}
{{{ a = -2}}}
{{{ b = 98 }}}
{{{ W[max] = -98/( 2*(-2) ) }}}
{{{ W[max] = 24.5 }}}
Put this value back into equation to get {{{ A[max] }}}
{{{ A[max] = -2*24.5^2 + 98*24.5 }}}
{{{ A[max] = -1200.5 + 2401 }}}
{{{ A[max] = 1200.5 }}} m2
The maximum area is 1200.5 m2
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Here's the plot:
{{{ graph( 400, 400, -5, 50, -140, 1300, -2x^2 + 98x ) }}} 
check my math!