Final answer:
In a parallelogram, the lengths of opposite sides are equal. Using the formula for the length of the diagonal, we can determine that the length of one of the diagonals cannot be 2 cm. The correct answer is No, it is not possible (b).
Step-by-step explanation:
In a parallelogram, the lengths of opposite sides are equal. Therefore, if the side lengths of the parallelogram are 4 cm and 7 cm, then the opposite sides are also 4 cm and 7 cm.
Since the length of a diagonal of a parallelogram is the square root of the sum of the squares of the two opposite sides, we can calculate the length of the diagonals of the parallelogram using the formula:
Length of Diagonal = √(Side1^2 + Side2^2)
= √(4^2 + 7^2)
= √65
≈ 8.06 cm
Therefore, the length of one of the diagonals cannot be 2 cm. The correct answer is No, it is not possible (b).