Answer: (A) [tex]12+12\sqrt{12}[/tex] .
Step-by-step explanation:
Perimter is the sum of the all sides of a figure.
As the given design has three exactly same or identical triangles with side-lengths [tex]2\sqrt{2}\ in, 2\sqrt{2}\ in, 4\ in[/tex] joined by ending vertices.
Then, the combined operimetr of thge design would be :
3 x (Perimeter of the one triangle)
For this , Perimeter of one triangle = [tex]2\sqrt{2}+2\sqrt{2}+4\ in =(4\sqrt{2}+4) = 4(\sqrt{2}+1) \ in[/tex]
Now , the combined operimetr of thge design would be :
[tex]3\times4(\sqrt{2}+1)=12(\sqrt{2}+1)\ in[/tex] or [tex]12+12\sqrt{12}\ in[/tex]
Hence, the correct option is (A) [tex]12+12\sqrt{12}[/tex] .
