1. What is the Length of Rectangle Formula?

This calculator computes the length of a rectangle when given its area and the diameter of its circumcircle. The formula derives from the geometric relationships between a rectangle's dimensions, area, and its circumscribed circle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Length of the rectangle (m)
• \( D_c \) — Diameter of the circumcircle (m)
• \( A \) — Area of the rectangle (m²)

Explanation: The formula combines the Pythagorean theorem and the area formula to solve for the rectangle's length.

3. Mathematical Explanation

Details: For a rectangle with length l and width w, the diameter of the circumcircle equals the diagonal: \( D_c = \sqrt{l^2 + w^2} \). The area is \( A = l \times w \). Solving these equations simultaneously yields the given formula.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle and area of the rectangle. Both values must be positive numbers. The calculator will compute the corresponding length.

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. Its diameter equals the rectangle's diagonal.

Q2: Why does the formula have two square roots?
A: The inner square root handles the relationship between area and diagonal, while the outer square root solves for the length dimension.

Q3: What if I get an error message?
A: An error occurs when \( D_c^4 < 4A^2 \), which is mathematically impossible for a real rectangle. Check your input values.

Q4: Can this formula be used for squares?
A: Yes, for a square (where l = w), the formula simplifies appropriately and will give correct results.

Q5: What units should I use?
A: Use consistent units (e.g., meters for length/diameter, square meters for area). The result will be in the same length unit as the diameter input.