Explanation:

Sure! Let's go over the statements and options:

- Question: Are the diagonals of a parallelogram perpendicular to each other?

- Statement I: The parallelogram has all sides of equal length.

- This indicates that the parallelogram is a rhombus. In a rhombus, the diagonals are always perpendicular to each other.

- Statement II: The parallelogram is a rectangle.

- In a rectangle, the diagonals are equal but not necessarily perpendicular unless it's a square.

- Option 1: If the question can be answered using one statement alone but not the other.

- Statement I is sufficient because in a rhombus, diagonals are perpendicular. Statement II is not sufficient alone because a rectangle doesn't guarantee perpendicular diagonals.

- Option 2: If the question can be answered by using either statement alone.

- Incorrect, since only Statement I alone gives the answer.

- Option 3: If the question can be answered using both statements together, but not alone.

- Incorrect, as Statement I alone answers the question.

- Option 4: If the question cannot be answered even by using both statements together.

- Incorrect, as Statement I already provides a definite answer.