Question 432524
Call the length {{{ x }}}
The formula is:
{{{ 2/x = x/(x+2) }}}
Multiply both sides by {{{ x*(x+2) }}}
{{{ 2*(x+2) = x^2 }}}
{{{ 2x + 4 = x^2 }}}
{{{ x^2 - 2x - 4 = 0 }}}
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a= 1}}}
{{{b = -2}}}
{{{c = -4}}}
 {{{x = (-(-2) +- sqrt( (-2)^2-4*1*(-4) ))/(2*1) }}}
{{{x = ( 2 +- sqrt( 4 + 16 ))/2 }}}
{{{ x = (2 +- sqrt( 4*5))/2 }}}
{{{ x = 2/2 + 2*sqrt(5)/2 }}}
{{{ x= 1 + sqrt(5) }}}
The other root is negative, so it can't be used
The area is {{{A = x*2}}}
{{{ A = 2*(1 + sqrt(5))}}}
{{{ A = 2 + 2*sqrt(5) }}} in.