Answer
$6+6\sqrt 2$ cm
Work Step by Step
$x^2+x^2=(6+x)^2$
$2x^2=(6+x)(6+x)$
$2x^2=6*6+6*x+x*6+x*x$
$2x^2=36+12x+x^2$
$2x^2=x^2+12x+36$
$2x^2-2x^2= x^2+12x+36-2x^2$
$0=-x^2+12x+36$
$0*-1=-1(-x^2+12x+36)$
$0=x^2-12x-36$
$0+36=x^2-12x-36+36$
$36=x^2-12x$
$36+(-12/2)^2=x^2-12x+(-12/2)^2$
$36+(-6)^2=x^2-12x+(-6)^2$
$36+36=x^2-12x+36$
$72=(x-6)^2$
$\sqrt {72}=\sqrt {(x-6)^2}$
$±6\sqrt 2=(x-6)$
We can’t have a negative length, so we ignore the negative value.
$±6\sqrt 2=(x-6)$
$6\sqrt 2=x-6$
$6+6\sqrt 2=x-6+6$
$6+6\sqrt 2=x$
