1. What is the Length of Rectangle Formula?

The formula calculates the length of a rectangle when given its perimeter and the diameter of its circumcircle. This relationship is derived from geometric properties of rectangles and their circumscribed circles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Length of the rectangle (m)
• \( P \) — Perimeter of the rectangle (m)
• \( Dc \) — Diameter of the circumcircle (m)

Explanation: The formula combines the perimeter and circumcircle diameter to determine the longer side (length) of the rectangle using geometric relationships.

3. Importance of Rectangle Length Calculation

Details: Calculating rectangle dimensions from perimeter and circumcircle properties is important in geometry problems, architectural design, and various engineering applications where these parameters are known.

4. Using the Calculator

Tips: Enter the perimeter and circumcircle diameter in meters. Both values must be positive numbers. The expression under the square root must be non-negative for a valid solution.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumcircle of a rectangle?
A: A circumcircle is a circle that passes through all four vertices of the rectangle. For a rectangle, the circumcircle's diameter equals the rectangle's diagonal.

Q2: Why does the square root expression become negative sometimes?
A: This happens when the input values are geometrically impossible (e.g., the circumcircle diameter is too small for the given perimeter).

Q3: Can this formula be used for squares?
A: Yes, for squares (where length = width), the formula will correctly calculate the side length.

Q4: What units should I use?
A: The calculator uses meters, but you can use any consistent unit as long as both inputs use the same unit.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact based on the geometric relationships, provided the input values are valid.