Question 433556
Let {{{w}}} = the width of the border
given:
the area of the garden is {{{3*3 = 9}}} m2
The dimensions of the garden plus the border are
{{{ (3 + 2w)*(3 + w) }}}
{{{ (3 + 2w)*(3 + w)  = 9 + 6w + 3w + 2w^2 }}}
{{{ 2w^2 + 9w + 9 = 2*9 }}}
{{{ 2w^2 + 9w - 9 = 0}}}
use the quadratic formula
{{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 2}}}
{{{b = 9}}}
{{{c = -9}}}
{{{w = (-9 +- sqrt( 9^2-4*2*(-9) ))/(2*2) }}}
{{{w = (-9 +- sqrt( 81 + 72 ))/4 }}}
{{{w = (-9 +- sqrt( 153 ))/4 }}}
{{{w = (-9 + 12.369)/4 }}}
{{{ w = 3.369/4 }}}
{{{ w = .842 }}} m