Breadth of Rectangle given Circumradius Calculator

Formula Used:

\[ b = \sqrt{4 \times r_c^2 - l^2} \]

Breadth of Rectangle:

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1. What is the Breadth of Rectangle given Circumradius Formula?

The formula calculates the breadth of a rectangle when its circumradius and length are known. The circumradius is the radius of the circle that passes through all four vertices of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \sqrt{4 \times r_c^2 - l^2} \]

Where:

\( b \) — Breadth of Rectangle (m)
\( r_c \) — Circumradius of Rectangle (m)
\( l \) — Length of Rectangle (m)

Explanation: The formula is derived from the relationship between the rectangle's dimensions and its circumradius, where the circumradius equals half the diagonal of the rectangle.

3. Importance of Rectangle Breadth Calculation

Details: Calculating the breadth of a rectangle given its circumradius and length is important in geometry, architecture, and engineering applications where rectangular shapes need to fit within circular boundaries or constraints.

4. Using the Calculator

Tips: Enter the circumradius and length in meters. Both values must be positive numbers, and the circumradius must be at least half the length of the rectangle for a valid solution.

5. Frequently Asked Questions (FAQ)

Q1: What is the circumradius of a rectangle?
A: The circumradius is the radius of the circle that passes through all four vertices of the rectangle. It equals half the length of the rectangle's diagonal.

Q2: Can this formula be used for squares?
A: Yes, for a square (where length equals breadth), the formula simplifies appropriately since both dimensions are equal.

Q3: What units should I use for the inputs?
A: The calculator uses meters, but you can use any consistent unit of length as long as all inputs use the same unit.

Q4: What if I get an error message?
A: The error indicates that the circumradius is too small for the given length. The circumradius must be at least half the length of the rectangle.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values. The result is rounded to 4 decimal places for practical use.