Question 838704
If the walkway is of uniform width, then I can say:
{{{ ( 30 - 2x )*( 20 - 2x ) = 400 }}}
{{{ 600 - 40x - 60x + 4x^2 = 400 }}}
{{{ 4x^2 - 100x + 200 = 0 }}}
{{{ x^2 - 25x + 50 = 0 }}}
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{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -25 }}}
{{{ c = 50 }}}
{{{ x = (-(-25) +- sqrt( (-25)^2 - 4*1*50 )) / (2*1) }}}
{{{ x = ( 25 +- sqrt( 625 - 200 )) / 2 }}}
{{{ x = ( 25 +- sqrt( 425 )) / 2 }}}
{{{ x = ( 25 +- 20.6155) / 2 }}} 
{{{ x = ( 25 - 20.6155 ) / 2 }}} 
{{{ x = 4.3845/2 }}}
{{{ x = 2.11922 }}}
Rounded off, the walkway is 2.12 ft wide
check:
{{{ ( 30 - 2x )*( 20 - 2x ) = 400 }}}
{{{ ( 30 - 2*2.1192 )*( 20 - 2*2.1192 ) = 400 }}}
{{{ ( 30 - 4.2384 )*( 20 - 4.2384 ) = 400 }}}
{{{ 25.7616*15.7616 = 400 }}}
{{{ 406.044 = 400 }}}
This is a pretty big error, so check my math,
but I think my method is OK