Final answer:
The perimeter of the rectangle is given by adding all four sides together. After simplification, the correct expression for the perimeter is 10.6c + 13.6d. However, this does not match any of the answer choices provided, indicating a potential error in the question or answer choices.
Step-by-step explanation:
The student's question deals with finding the expression that represents the perimeter of a rectangle. To find the perimeter of a rectangle, we add up the lengths of all four sides. If we let one pair of opposite sides be represented by the expression (3.4c - 2.7d), and the other pair by (1.9c + 9.5d), then the total perimeter P is the sum of these expressions multiplied by 2:
P = 2[(3.4c - 2.7d) + (1.9c + 9.5d)]
This simplifies to:
P = 2[3.4c + 1.9c - 2.7d + 9.5d]
P = 2[5.3c + 6.8d]
P = 10.6c + 13.6d
However, none of the answer choices provided matches this result. Hence, there might be a mistake in the question or in the provided answer choices. The student may need to recheck the values given for the sides of the rectangle or the answer choices.