Question

How does the length of the hypotenuse in a right triangle compare to the lengths of the legs?

Answer 1

In a right triangle, the length of the hypotenuse is always longer than the lengths of its legs. This is a direct result of the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse's length is equal to the sum of the squares of the lengths of the two legs. Mathematically, the theorem is expressed as:

c² = a² + b²

Where:
- c represents the length of the hypotenuse
- a and b represent the lengths of the legs

Since the lengths of a and b are squared and then added together to determine the length of the hypotenuse, it is evident that the hypotenuse will always be longer than either of the legs.