Question 482059
The original area was {{{ 9*6 = 54 }}} m2
Double this area is {{{  108 }}} m2
given:
{{{ 108 = ( 9 + x )*( 6 + x ) }}}
{{{ 108 = 54 + 6x + 9x + x^2 }}}
{{{ x^2 + 15x - 54 = 0 }}}
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = 15 }}}
{{{ c = -54 }}}
{{{x = (-15 +- sqrt( 15^2-4*1*(-54) ))/(2*1) }}} 
{{{x = (-15 +- sqrt( 225 + 216 )) / 2 }}} 
{{{x = (-15 +- sqrt( 441 )) / 2 }}} 
{{{ x = (-15 + 21) / 2 }}}
{{{ x = 6/2 }}}
{{{ x = 3 }}}
The final dimensions are {{{ 9 + 3 = 12 }}} and {{{ 6 + 3 = 9 }}}
= 12 m x 9 m
check:
{{{ 12*9 = 108 }}}
OK