1. What is the Diagonal of a Rectangle?

The diagonal of a rectangle is the straight line connecting two opposite corners. It divides the rectangle into two right-angled triangles and is the longest distance between any two points on the rectangle.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem:

Where:

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

Explanation: The formula comes from the Pythagorean theorem where the diagonal is the hypotenuse of a right triangle formed by the length and width.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal is important in construction, carpentry, screen size measurements, and any application where you need to know the longest dimension of a rectangular space or object.

4. Using the Calculator

Tips: Enter the length and width in the same units (inches, centimeters, feet, etc.). 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 units can be used (cm, inches, feet, meters) as long as both dimensions are in the same units.

Q3: Can this be used for 3D objects?
A: No, this is specifically for 2D rectangles. For 3D rectangular prisms, you would need the space diagonal formula.

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

Q5: What's the relationship between diagonal and aspect ratio?
A: The diagonal helps determine the aspect ratio (width:height) of screens and displays.