Question 200005
Draw  a  rough  sketch  of  the  rectangle.  Let  left  side  be  river,  perpendiculars  to  river  (a),  and  parallel  to  river (b).
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Perimeter  is  2a +b = 500,,,,,River  side  does  not  need  fence
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b= 500 -2a
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Area  of  rectangle  is  A= l*w = a*b
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making  a  quick  table
a,,,,,,,,,,,,,b,,,,,,,,,,,,,Area
0,,,,,,,,,,,225,,,,,,,,,,,,,,,,,,,,0
100,,,,,,,300,,,,,,,,,,,30,000
124,,,,,,,252,,,,,,,,,,,31,248
125,,,,,,,250,,,,,,,,,,,31,250,,,,,,,,,,max  area
126,,,,,,,248,,,,,,,,,,,31,248
200,,,,,,,100,,,,,,,,,,,20,000
250,,,,,,,,,,,0,,,,,,,,,,,,,,,,,,,,0
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dim  are  a=125,  b=25,  for  a  max  area  of  31,250 m^2