Question 878132
Using the Pythagorean theorem,
{{{x^2+(2x)^2=23^2}}}
{{{x^2+4x^2=23}}}
{{{5x^2=23}}}
{{{x^2=23/5}}}
{{{x=sqrt(23/5)}}}
{{{x=sqrt(115)/5}}}
The perimeter of the rectangle is 
{{{P=x+2x+2x+x=6x}}}
{{{P=(6/5)sqrt(115)}}}