Question 135538
Call the length of a side fenced with aluminum {{{a}}}
Call the length of a side fenced with steel {{{s}}}
{{{a*s = 1200}}} m2
The total length of aluminum fence = {{{2a}}}
The total length of steel fence = {{{2s}}}
{{{20*(2a) + 10*(2s) = 2200}}}
{{{40a + 20s = 2200}}}
{{{s = 1200/a}}}
{{{40a + 20*(1200/a) = 2200}}}
{{{40a^2 + 24000 = 2200a}}}
{{{a^2 - 55a + 600 = 0}}}
Use the quadratic formuala
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}} 
{{{b = -55}}}
{{{c = 600}}}
{{{x = (-(-55) +- sqrt( (-55)^2-4*1*600 ))/(2*1) }}}
{{{x = (55 +- sqrt( 3025 - 2400 ))/2 }}}
{{{x = (55 +- sqrt( 625 ))/2 }}}
{{{x = (55 +- 25)/2 }}}
{{{x = 40}}}
{{{x = 15}}}
If {{{a = 40}}}, then {{{s = 1200/a}}} and
{{{s = 30}}}
{{{40a + 20s = 2200}}}
{{{40*40 + 20*30 = 2200}}}
{{{1600 + 600 = 2200}}}
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If {{{a = 15}}}, then
{{{s = 80}}}
{{{40a + 20s = 2200}}}
{{{40*15 + 20*80 = 2200}}}
{{{600 + 1600 = 2200}}}
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The length of each side fenced with aluminum can be 40 m and the 
length of a side fenced with steel will be 30 m
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The length of the side fenced with aluminum can also be 15 m and
the length of a side fenced with steel will be 80 m