Breadth of Rectangle given Perimeter and Diameter of Circumcircle Calculator

Formula Used:

\[ b = \frac{1}{4} \times \left( P - \sqrt{(8 \times Dc^2) - P^2} \right) \]

Breadth of Rectangle:

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1. What is the Breadth of Rectangle Formula?

The formula calculates the breadth of a rectangle when given its perimeter and the diameter of its circumcircle. This mathematical relationship helps determine one dimension of a rectangle when the other dimension and circumcircle properties are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{1}{4} \times \left( P - \sqrt{(8 \times Dc^2) - P^2} \right) \]

Where:

\( b \) — Breadth of the rectangle (m)
\( P \) — Perimeter of the rectangle (m)
\( Dc \) — Diameter of the circumcircle (m)

Explanation: The formula derives from the geometric relationships between a rectangle's dimensions, its perimeter, and the diameter of its circumscribing circle.

3. Importance of Rectangle Breadth Calculation

Details: Calculating the breadth of a rectangle is essential in various geometric applications, construction projects, and engineering designs where rectangular shapes are involved.

4. Using the Calculator

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

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 a rectangle. For a rectangle, the diameter of the circumcircle equals the diagonal of the rectangle.

Q2: Why does the formula include a square root?
A: The square root comes from the Pythagorean theorem applied to the relationship between the rectangle's sides, diagonal, and perimeter.

Q3: What if I get a negative value under the square root?
A: This indicates that the input values are inconsistent - no rectangle exists with the given perimeter and circumcircle diameter combination.

Q4: Can this formula be used for squares?
A: Yes, squares are special cases of rectangles, so the formula applies to squares as well.

Q5: What are practical applications of this calculation?
A: This calculation is useful in architecture, engineering, carpentry, and any field dealing with rectangular shapes and their geometric properties.