Which of the following sets could be the sides of a right triangle?

To determine if a set of three lengths can form a right triangle, we can use the Pythagorean theorem. According to this theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

For instance, if we have the three lengths: a, b, and c, where c is the longest side, then they can form a right triangle if:

c² = a² + b²

Let’s consider some examples:

• If we have the set (3, 4, 5):

Here, 5 is the longest side. Checking the Pythagorean theorem:

5² = 3² + 4²

25 = 9 + 16

25 = 25 ✔️

• If we take the set (1, 1, √2):

The longest side is √2. Checking the theorem:

(√2)² = 1² + 1²

2 = 1 + 1

2 = 2 ✔️

By testing different sets of numbers in this way, you can determine which sets satisfy the Pythagorean theorem, confirming whether they can indeed be the sides of a right triangle.