Answer: Perimeter and Area of the final poster will be 168 cm and 1728 cm² respectively.
Step-by-step explanation:
Since we have given that
Each student is to design a school poster.
Dimensions of rectangle are :
[tex]12\ cm\ by\ 16\ cm[/tex]
It is then dilated by a scale factor of 3.
So, Perimeter of the final poster becomes
[tex]3\times 2\times (L+B)\\\\=6(12+16)\\\\=6\times 28\\\\=168\ cm[/tex]
Similarly, Area of the final poster becomes
[tex]3^2\times L\times B\\\\=9\times 12\times 16\\\\=1728\ cm^2[/tex]
Hence, Perimeter and Area of the final poster will be 168 cm and 1728 cm² respectively.