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The inradius of an isosceles right triangle is the radius of the largest circle that can fit inside the triangle, tangent to all three sides. It represents the distance from the center of the inscribed circle to any of the triangle's sides.
The calculator uses the formula:
Where:
Explanation: This formula derives from the relationship between the perimeter and the inradius in an isosceles right triangle, where the denominator represents a constant factor specific to this triangle type.
Details: Calculating the inradius is important in geometry for determining the size of the inscribed circle, which has applications in various fields including engineering, architecture, and design where circular components need to fit within triangular spaces.
Tips: Enter the perimeter of the isosceles right triangle in meters. The value must be positive and greater than zero. The calculator will compute the inradius based on the mathematical relationship.
Q1: What is an isosceles right triangle?
A: An isosceles right triangle is a triangle with two equal sides that form a right angle (90 degrees), making it both isosceles and right-angled.
Q2: Why is there a square root of 2 in the formula?
A: The square root of 2 appears naturally in right triangles due to the Pythagorean theorem, particularly in triangles with 45-45-90 degree angles.
Q3: Can this formula be used for other types of triangles?
A: No, this specific formula applies only to isosceles right triangles. Other triangle types have different formulas for calculating inradius.
Q4: What are the units for the inradius?
A: The inradius will have the same units as the perimeter input. If perimeter is in meters, the inradius will be in meters.
Q5: How accurate is the calculation?
A: The calculation is mathematically exact based on the formula. The accuracy depends on the precision of the input value.