1. What is the Perimeter of Isosceles Right Triangle?

The Perimeter of an Isosceles Right Triangle is the total distance around the edge of the triangle. For an isosceles right triangle, the perimeter can be calculated using the inradius through the formula: \( P = (2 + \sqrt{2})^2 \times r_i \).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( P \) — Perimeter of Isosceles Right Triangle (m)
• \( r_i \) — Inradius of Isosceles Right Triangle (m)
• \( \sqrt{2} \) — Square root of 2, approximately 1.4142

Explanation: The formula relates the perimeter of an isosceles right triangle to its inradius, incorporating the mathematical constant \( \sqrt{2} \) which is characteristic of right triangles.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter is essential in various geometric and real-world applications, including construction, design, and any scenario requiring boundary measurement of triangular shapes.

4. Using the Calculator

Tips: Enter the inradius value in meters. Ensure the value is positive and valid for accurate results.

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, making the angles 45°, 45°, and 90°.

Q2: What is the Inradius?
A: The inradius is the radius of the circle inscribed within the triangle, tangent to all three sides.

Q3: Why is \( \sqrt{2} \) used in the formula?
A: \( \sqrt{2} \) appears due to the properties of the isosceles right triangle, specifically the ratio between the hypotenuse and the legs.

Q4: Can this formula be used for other types of triangles?
A: No, this formula is specific to isosceles right triangles. Other triangles have different perimeter formulas.

Q5: What are the units of measurement?
A: The perimeter and inradius are typically measured in meters (m), but any consistent unit can be used as long as it's the same for both values.