Question 1141591
The rug + the border must fit in the 10 x 15 room
Let {{{ A }}} = the area of the rug
Let {{{ x }}} = the width of the border
{{{ A = ( 10 - 2x )*( 15 - 2x ) }}}
{{{ A = 150 - 30x - 20x + 4x^2 }}}
{{{ A = 4x^2 - 50x + 150 }}}
{{{ A = 100 }}} ft2
{{{ 100 = 4x^2 - 50x + 150 }}}
{{{ 4x^2 - 50x + 50 = 0 }}}
{{{ 2x^2 - 25x + 25 = 0 }}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 2 }}}
{{{ b = -25 }}}
{{{ c = 25 }}}
{{{ x = (-(-25) +- sqrt( 625 - 4*2*25 ))/4 }}}
{{{ x = ( 25 +-sqrt( 625 - 200 ))/4 }}}
{{{ x = ( 25 - sqrt( 425 ))/4 }}}
{{{ x = ( 25 - 20.6155 )/4 }}}
{{{ x = 4.3845/4 }}}
{{{ x = 1.0961 }}} ft is the minimum width of the border
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check:
{{{ A = ( 10 - 2x )*( 15 - 2x ) }}}
{{{ 100 = ( 10 - 2x )*( 15 - 2x ) }}}
{{{ 100 = ( 10 - 2*1.0961 )*( 15 - 2*1.0961 ) }}}
{{{ 100 = ( 10 - 2.1922 )*( 15 - 2.1922 ) }}}
{{{ 100 = 7.8078*12.8078 }}}
{{{ 100 = 100.00074 }}}
error due to rounding off
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get a 2nd opinion if needed