Question 286594
Let the length of the side bordering the river = {{{y}}}
Let the 2 sides perpendicular to the side bordering the river = {{{x}}}
given:
a){{{A = xy}}} m2
{{{P = 300 + y}}}
b){{{P= 2x + 2y}}} m
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{{{2x = 300 - y}}}
{{{y = 300 - 2x}}}
{{{A = x*(300 - 2x)}}}
c){{{A = 300x - 2x^2}}}
{{{x}}} is a maximum halfway between the 2 roots. First I'll find the roots
{{{x*(2x - 300) = 0}}}
The roots are {{{x = 0}}} and
{{{2x - 300 = 0}}}
{{{2x = 300}}}
{{{x = 150}}}
The midpoint is {{{x = 75}}}
{{{y = 300 - 2x}}}
{{{y = 300 - 150}}}
{{{y = 150}}}
d)The dimensions that maximize area are 75 x 150
check:
Just vary the dimensions a little bit, and Area should decrease
{{{A = 75*150}}}
{{{A = 11250}}} m2
Suppose:
{{{A2 = 76*148}}} -note that {{{2*76 + 148 = 152 + 148}}} 
and {{{152+ 148 = 300}}}  as it should
{{{A2 = 11248}}} It decreased by {{{2}}} m
OK