Final answer:
The perimeter of the outside of the frame is found by adding a 2-inch border to each dimension of the mirror and then calculating the perimeter of the resulting rectangle. After calculations, the perimeter is determined to be 68 inches (option D).
Step-by-step explanation:
To find the perimeter of the outside of the frame for a rectangular mirror, first we determine the dimensions of the mirror including the frame. The mirror has a length of 14 inches and an area of 168 square inches, which allows us to find the width of the mirror through the equation area = length × width. Therefore, the width of the mirror is 168 square inches / 14 inches = 12 inches. Since the frame is 2 inches wide, it adds an extra 4 inches to both the length and the width of the mirror (2 inches on each side).
The length of the mirror including the frame is 14 inches + 4 inches = 18 inches, and the width is 12 inches + 4 inches = 16 inches. The perimeter of a rectangle is calculated by adding the lengths of all four sides. Thus, the perimeter of the outside of the frame is 2 × (length + width) = 2 × (18 inches + 16 inches) = 2 × 34 inches = 68 inches.
The correct answer for the perimeter of the outside of the frame is 68 inches, which is option D.