1. What is the Hypotenuse of an 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 is √2 times the length of each leg.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Perimeter \) — Total distance around the triangle (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula derives from the relationship between the perimeter and the sides of an isosceles right triangle, where the perimeter equals the sum of two equal legs plus the hypotenuse.

3. Importance of Hypotenuse Calculation

Details: Calculating the hypotenuse is essential in geometry, construction, and various engineering applications where right triangles are used. It helps determine the longest side when the perimeter is known.

4. Using the Calculator

Tips: Enter the perimeter of the isosceles right triangle in meters. The value must be positive and greater than zero.

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 at the base both 45 degrees.

Q2: Why is the formula H = P/(1+√2) used?
A: This formula comes from the perimeter expression P = 2a + H, where a is the leg length, and H = a√2. Substituting gives P = H/√2 * 2 + H = H(2/√2 + 1) = H(√2 + 1).

Q3: Can this calculator be used for non-isosceles right triangles?
A: No, this formula is specific 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 perimeter (typically meters).

Q5: How accurate is the calculation?
A: The calculation is mathematically exact. The displayed result is rounded to 6 decimal places for practical use.