1. What is the Rectangle Diagonal Formula?

The diagonal of a rectangle can be calculated using the Pythagorean theorem, which relates the sides of a right triangle to its hypotenuse (the diagonal in this case).

2. How Does the Calculator Work?

The calculator uses the diagonal formula:

Where:

• \( d \) — Diagonal of the rectangle
• \( l \) — Length of the rectangle
• \( w \) — Width of the rectangle

Explanation: The formula comes from applying the Pythagorean theorem to the right triangle formed by the length, width, and diagonal of the rectangle.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal is important in construction, design, and various engineering applications where precise measurements of rectangular spaces are needed.

4. Using the Calculator

Tips: Enter the length and width in the same units (e.g., inches, centimeters, meters). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for squares?
A: Yes, for squares (where length = width), the formula simplifies to \( d = l\sqrt{2} \).

Q2: What units should I use?
A: Any consistent length units can be used (inches, cm, meters, etc.), as long as both dimensions are in the same units.

Q3: Can this be used for 3D boxes?
A: No, this is for 2D rectangles. For 3D boxes, you would need the space diagonal formula: \( \sqrt{l^2 + w^2 + h^2} \).

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming perfect right angles and precise measurements of length and width.

Q5: What's the practical use of knowing a rectangle's diagonal?
A: Diagonals are used in construction for checking squareness, in screen size measurements, and in various design applications.