Answer
$-3*(1-\sqrt5)/2$
Work Step by Step
3 inches long
$(1+\sqrt5)/2$
$(1+\sqrt5)/2=3/x$
$6 = (1+\sqrt5)x$
$6/(1+\sqrt5) = (1+\sqrt5)x/(1+\sqrt5)$
$6/(1+\sqrt5) = x$
$6/(1+\sqrt5)$
$6/(1+\sqrt5) *(1-\sqrt5)/(1-\sqrt5))$
$6*(1-\sqrt5)/(1-\sqrt5+\sqrt5-5)$
$6*(1-\sqrt5)/-4$
$-3*(1-\sqrt5)/2$