Question 481007
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Hi,
Each side of a square is 4 m long, therefore A = 16m^2
When each side is increased by x, then (4+x)(4+x) = 32m^2
 (4+x)(4+x) = 32m^2
  16 + 8x + x^2 = 32
  x^2 + 8x - 16 = 0
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-8 +- sqrt( 128))/(2) }}} 
tossing out negative solution for number of meters
 x = 1.6569m

CHECKING our Answer***
  5.6569*5.6569 = 32m^2