Question 1048668
Let {{{ x }}} = the width of the border
{{{ ( 21 - 2x )*( 24 - 2x ) = 238 }}}
( do you see why I subtracted {{{ 2x }}} from each dimension ? )
{{{ 504 - 48x - 42x + 4x^2 = 238 }}}
{{{ 4x^2 - 90x + 266 = 0 }}}
{{{ 2x^2 - 45x + 133 = 0 }}}
Use quadratic formula
{{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 2 }}}
{{{ b = -45 }}}
{{{ c = 133 }}}
{{{ x = (-(-45) +- sqrt( (-45)^2-4*2*133 ))/(2*2) }}}
{{{ x = ( 45 +- sqrt( 2025 - 1064 )) / 4 }}}
{{{ x = ( 45 +- sqrt( 961 )) / 4 }}}
{{{ x = ( 45 - 31 ) / 4 }}} ( only the minus square root works here )
{{{ x = 14/4 }}}
{{{ x = 7/2 }}}
{{{ x = 3.5 }}}
The border is 3.5 ft wide
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check:
{{{ ( 21 - 2x )*( 24 - 2x ) = 238 }}}
{{{ ( 21 - 2*(7/2) )*( 24 - 2*(7/2) ) = 238 }}}
{{{ ( 21 - 7 )*( 24 - 7 ) = 238 }}}
{{{ 14*17 = 238 }}}
{{{ 238 = 238 }}}
OK