Question 164437
Call the side parallel to the building {{{x}}} ft
Then the remaining 2 sides would each be
{{{(800 - x)/2}}} ft
The area can then be expressed as
{{{A = x*(800 - x)/2}}}
{{{A = (800x - x^2) / 2}}}
{{{A = 400x - x^2/2}}}
This is a parabola which, because the coefficient of
{{{x^2}}} is negative, has a maximum and not a minimum
The maximum is at {{{-(b/2a)}}}
{{{a = -(1/2)}}}
{{{b = 400}}}
{{{-(b/2a) = -(400/-1)}}}
{{{-(400)/-1 = 400}}}
The maximum area is 400 ft2
I'll check by finding {{{x}}}
{{{A = 400x - x^2/2}}}
{{{400 = 400x - x^2/2}}}
{{{-x^2/2 + 400x - 400 = 0}}}
{{{-x^2 + 800x - 800 = 0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = -1}}}
{{{b = 800}}}
{{{c = -800}}}
{{{x = (-800 +- sqrt( 800^2-4*(-1)*(-800) ))/(2*(-1)) }}}
{{{x = (-800 +- sqrt( 640000 - 3200 ))/-2) }}}
{{{x = (-800 +- sqrt( 636800 ))/-2) }}}
{{{x = (-800 +- 797.997)/-2) }}}
If I use the (+) value of the square root, I get too small a value
for {{{x}}}, so I'll use the (-) square root
{{{x = -1597.997/-2}}}
{{{x = 798.998}}}
The remaining sides are 
{{{1.002/2 - .501}}}each
{{{A = 798.998*.501}}}
{{{A = 400.297}}} The error is due to rounding off, I think