Answer
$P=(3+\sqrt5)x$
Work Step by Step
The shorter leg is $x$ and the longer one is twice the shorter one, or $2x$. We also know that according to the Pythagorean Theorem, the third side is:
$c^2=a^2+b^2$
$c^2=x^2+(2x)^2$
$c=\sqrt{x^2+(2x)^2}=\sqrt5 x$
Hence, the perimeter is (the sum of all sides):
$P=x+2x+\sqrt5x=(3+\sqrt5)x$
