The inches of ribbon that Mrs. Martin needs will be equal to the perimeter of the rectangular mirror.
We know that the area of a rectangle equals the length times the width.
Area = length * width
324 square inches = length * 12 inches
length = 27 inches
The perimeter of a rectangle is two times the length plus two times the width.
Perimeter = length + length + width + width
Perimeter = 27 + 27 + 12 + 12
Perimeter = 54 + 24
Perimeter = 78 inches
Therefore, Mrs. Martin needs 78 inches of ribbon.