Answer
$6+6\sqrt 2$ cm
Work Step by Step
$x^2+x^2=(x+6)^2$
$2x^2=(x+6)(x+6)$
$2x^2=x*x+x*6+6*x+6*6$
$2x^2=x^2+12x+36$
$2x^2-2x^2=x^2+12x+36-2x^2$
$-x^2+12x+36=0$
$a=-1$, $b=12$, $c=36$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-12±\sqrt {12^2-4*-1*36})/2*-1$
$x=(-12±\sqrt {144+144})/-2$
$x=(-12±\sqrt {288})/-2$
$x=(-12±\sqrt 2*\sqrt{144})/-2$
$x=(-12±12\sqrt 2)/-2$
$x=(-12+12\sqrt 2)/-2$
$x=(6-6\sqrt 2)$
We know 6-6\sqrt 2 is less than 0, so we ignore this answer. We can’t have a negative distance.
$x=(-12-12\sqrt 2)/-2$
$x=6+6\sqrt 2$
