<PRE><B>Question 347264</B>
2*4^2=(4+x)^2
2*16=16+8x+x^2
x^2+8x+16-32=0
x^2+8x-16=0
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
x=(-8+-sqrt[8^2-4*1*-16])/2*1
x=(-8+-sqrt[64+64])/2
x=(-8+-sqrt128)/2
x=(-8+-11.314)/2
x=(-8+11.314)/
x=3.314/2
x=1.657 ans. for the increased length of the sides.
Proof:
2*4^2=(4+1.657)^2
2*16=5.657^2
32=32 </PRE>