Question 1097710
Let {{{ W }}} = the width of the field
Let {{{ L }}} = the length of the field
{{{ 2L + 2W = 400 }}}
{{{ 2L = 400 - 2W }}}
{{{ L = 200 - W }}}
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Now I can say:
{{{ W*( 200 - W ) = 8000 }}}
{{{ -W^2 + 200W - 8000 = 0 }}}
Use qudratic formula
{{{ W = ( -b +-sqrt( b^2 - 4*a*c ))/(2a) }}}
{{{ a = -1 }}}
{{{ b = 200 }}}
{{{ c = -8000 }}}
{{{ W = ( -200 +-sqrt( 40000 - 4*(-1)*(-8000) ))/(2*(-1)) }}}
{{{ W = ( -200 +-sqrt( 40000 - 32000 ))/(-2) }}}
{{{ W = ( -200 +-sqrt( 8000 ) ) /(-2) }}}
{{{ W = ( -200 + 89.443 ) / (-2) }}}
This solution doesn't work since you end up with negative answer, so
{{{ W = ( -200 - 89.443 ) / (-2) }}}
{{{ W = ( -289.443 ) / (-2) }}}
{{{ W = 144.7 }}}
{{{ L = 200 - W }}}
{{{ L = 200 - 144.7 }}}
{{{ L = 55.3 }}}
The field is 55.3 by 144.7
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Check answer:
{{{ L*W = 8000 }}}
{{{ 55.3*144.7 = 8000 }}}
{{{ 8001.91 = 8000 }}}
Error due to rounding off, think
also:
{{{ 2W + 2L = 400 }}}
{{{ 2*144.7 + 2*55.3 = 400 }}}
{{{ 289.4 + 110.6 = 400 }}}
{{{ 400 = 400 }}}
OK