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 from the area using the formula: Hypotenuse = 2 × √(Area).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Area \) — Area of the isosceles right triangle (m²)
• \( \sqrt{} \) — Square root function

Explanation: This formula derives from the relationship between the area and side lengths of an isosceles right triangle, where the area equals half the square of either leg, and the hypotenuse equals the leg multiplied by √2.

3. Importance of Hypotenuse Calculation

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

4. Using the Calculator

Tips: Enter the area of the isosceles right triangle in square 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 opposite those legs equal (45° each).

Q2: Why is the formula Hypotenuse = 2 × √(Area)?
A: In an isosceles right triangle, Area = (1/2) × leg². So leg = √(2 × Area). Then hypotenuse = leg × √2 = √(2 × Area) × √2 = 2 × √(Area).

Q3: Can this formula be used for any right triangle?
A: No, this specific formula applies only to isosceles right triangles where the two legs are equal.

Q4: What units should I use for area?
A: The calculator uses square meters, but the formula works with any consistent area unit (the hypotenuse will be in the corresponding length unit).

Q5: What if I know the leg length instead of area?
A: If you know the leg length (a), then hypotenuse = a × √2, and area = (1/2) × a².