Question 897639
Let {{{ p }}} = area of the pool in m2
Let {{{ d }}} = area of the deck in m2
-------------
given:
{{{ p + d = p + 140 }}} m2
The area of the pool plus the deck is:
{{{ p + d = ( w + 2 )*( w + 7 ) }}}
{{{ ( w + 2 )*( w + 7 ) = p + 140 }}}
{{{ p = ( w + 2 )*( w + 7 ) - 140 }}}
The width has to be greater than {{{ 7.594  }}} m
The length is greater than {{{ 12.594 }}} m
since 
{{{ w^2 + 9w + 14 = 140 }}}
{{{ w^2 + 9w - 126 = 0 }}}
{{{ w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = 9 }}}
{{{ c = -126 }}}
{{{ w = ( -9 +- sqrt( 9^2 - 4*1*(-126) ))/(2*1) }}}
{{{ w = ( -9 +- sqrt( 81 + 504 )) / 2 }}}
{{{ w = ( -9 + sqrt( 585 ) ) / 2 }}}
{{{ w = ( -9 + 24.187 ) / 2 }}}
{{{ w = 15.187 / 2 }}}
{{{ w = 7.594 }}}
----------------
check:
{{{ w^2 + 9w + 14 = 140 }}}
{{{ 7.594^2 + 9*7.594 + 14 = 140 }}}
{{{ 57.661 + 68.3415 + 14 = 140 }}}
{{{ 140.0025 = 140  }}}
close enough