Isosceles Right Triangle with Equal Perimeter and Area

The perimeter of an isosceles right triangle (in units) is numerically equal to its area (in square units.) What is the length of the hypotenuse? The answer is in the form $a+b\sqrt{c}$ where $a$, $b$, $c$ are positive integers, and $c$ is square-free. Input the value of $a+b+c$.