Answer:
D. [tex]4\sqrt{a^{2}+b^{2}}[/tex]
Step-by-step 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
[tex]a^{2} +b^{2} =C^{2}[/tex]
(C represents the hypotenuse)
So the hypotenuse can be written as [tex]\sqrt{a^{2} +b^{2} }[/tex]
Since four of these lines make up the perimeter,
the total perimeter will be [tex]4\sqrt{a^{2}+b^{2}}[/tex]
