Question 898084
Let {{{ x }}} = the width of the uniform border
{{{ x }}} gets added twice to both dimensions, so
I can say:
{{{ 3*4 + 18 = ( 3 + 2x )*( 4 + 2x ) }}}
{{{ 30 = 12 + 8x + 6x + 4x^2 }}}
{{{ 4x^2 + 14x - 18 = 0 }}}
{{{ 2x^2 + 7x - 9 = 0 }}}
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Use the quadratic formula:
{{{ x = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 2 }}}
{{{ b = 7 }}}
{{{ c = -9 }}}
{{{ x = ( -7 +- sqrt( 7^2 - 4*2*(-9) )) / (2*2) }}}
{{{ x = ( -7 +- sqrt( 49 + 72 )) / 4 }}}
{{{ x = ( -7 + sqrt( 121 )) / 4 }}}
{{{ x = ( -7 + 11 ) / 4 }}}
{{{ x = 4/4 }}}
{{{ x = 1 }}}
The width of the border is 1 ft
check:
{{{ 30 = 12 + 8x + 6x + 4x^2 }}}
{{{ 30 = 12 + 8*1 + 6*1 + 4*1 }}}
{{{ 30 = 12 + 8 + 6 + 4 }}}
{{{ 30 = 30 }}}
OK