1. What is the Hypotenuse of Isosceles Right Triangle?

The hypotenuse of an isosceles right triangle is the longest side opposite the right angle. In an isosceles right triangle, the two legs are equal in length, and the hypotenuse can be calculated using the Pythagorean theorem or specialized formulas.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Inradius \) — The radius of the inscribed circle (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula relates the hypotenuse length to the inradius of an isosceles right triangle through a constant factor derived from the geometric properties of the triangle.

3. Importance of Hypotenuse Calculation

Details: Calculating the hypotenuse is essential in various geometric applications, construction projects, and mathematical problems involving right triangles. It helps determine the longest side when the inradius is known.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an isosceles right triangle?
A: An isosceles right triangle is a right triangle with two equal legs and angles of 45°, 45°, and 90°.

Q2: How is this formula derived?
A: The formula is derived from the relationship between the inradius and the sides of the triangle using geometric properties and the Pythagorean theorem.

Q3: Can this calculator be used for other types of triangles?
A: No, this specific formula applies only to isosceles right triangles where both legs are equal.

Q4: What are the units for the result?
A: The result is in the same units as the input (meters if inradius is in meters).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input value, though practical measurements may have some error.