Diagonals of a rectangle are perpendicular to each other.

Answer

To determine whether the statement "Diagonals of a rectangle are perpendicular to each other" is true or false, we can analyze the properties of a rectangle step by step.

### Step-by-Step Solution:

1. **Definition of a Rectangle**:
- A rectangle is a quadrilateral with opposite sides that are equal and all interior angles measuring 90 degrees.

2. **Properties of Diagonals in a Rectangle**:
- In a rectangle, the diagonals are equal in length. This can be derived from the Pythagorean theorem.
- The length of each diagonal can be calculated using the formula:
\[ d = \sqrt{L^2 + B^2} \]
where \(L\) is the length and \(B\) is the breadth of the rectangle.

3. **Analysis of Perpendicularity**:
- For two lines (or diagonals in this case) to be perpendicular, they must intersect at a right angle (90 degrees).
- In a rectangle, while the diagonals bisect each other (they meet at the midpoint), they do not intersect at right angles.

4. **Conclusion**:
- Since the diagonals of a rectangle do not intersect at right angles, the statement "Diagonals of a rectangle are perpendicular to each other" is **false**.

### Summary:
The diagonals of a rectangle are equal in length but are not perpendicular to each other.