Answer
[tex]P=28\sqrt{3}[/tex]
Explanation
The perimeter is the addition of all the side's lengths.
As this is a rectangle, one pair of sides measures 4√27, and the other pair measures √12. Then, the perimeter P can be calculated as follows:
[tex]P=\sqrt{12}+\sqrt{12}+4\sqrt{27}+4\sqrt{27}[/tex]
Simplifying:
[tex]P=2\sqrt{12}+8\sqrt{27}[/tex]
Now, we can further simplify by finding the factors of the numbers inside the square root:
[tex]12=6\cdot2=3\cdot2\cdot2=3\cdot2^2[/tex][tex]27=9\cdot3=3\cdot3\cdot3=3^2\cdot3[/tex]
Then, substituting the factors inside the square root in the perimeter equation and simplifying:
[tex]P=2\sqrt{3\cdot2^2}+8\sqrt{3^2\cdot3}[/tex][tex]P=2\cdot2\sqrt{3}+8\cdot3\sqrt{3}[/tex][tex]P=4\sqrt{3}+24\sqrt{3}[/tex][tex]P=28\sqrt{3}[/tex]
