Answer:
D.
![4\sqrt{a^(2)+b^(2)}](https://img.qammunity.org/2020/formulas/mathematics/high-school/5d0r6io8nlxhe56i85l1yut9g8knfi4dpc.png)
Explanation:
We can see the shape can be cut into 4 right triangles. We can use pythagoreans theorem to find the length of the hypotenuse.
The distance from 0 to a represents one side, and the distance from 0 to b represents the other side.
So
![a^(2) +b^(2) =C^(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/fotx03dkapqc4z0lyr54lfp9su777u0vqw.png)
(C represents the hypotenuse)
So the hypotenuse can be written as
![\sqrt{a^(2) +b^(2) }](https://img.qammunity.org/2020/formulas/mathematics/high-school/sv1ylqlmwntgvnnloswb7hp7gejngtdskc.png)
Since four of these lines make up the perimeter,
the total perimeter will be
![4\sqrt{a^(2)+b^(2)}](https://img.qammunity.org/2020/formulas/mathematics/high-school/5d0r6io8nlxhe56i85l1yut9g8knfi4dpc.png)