Question 363811
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Hi, 
Let x represent the length of each side of the square. (x+12ft) the diagonal.
applying the Pythagorean theorem (with the diagonal being the hypotenuse)
x^2 + x^2 = (x + 12)^2
2x^2 = x^2 + 24x + 144ft^2
x^2 -24x - 144  = 0
using the quadratic equation to solve
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (24 +- sqrt( 1152 ))/(2) }}}
{{{x = (24 +- sqrt( 64*18 ))/(2) }}}
{{{x = (24 +- 8*sqrt( 18 ))/(2) }}}
{{{x = 12+- 4*sqrt( 18 )}}}
{{{x = 12+- 16.971}}}
x = 28.971
x = -4.971