Question

Which side lengths form a right triangle?

1) [2, 2, sqrt4]
2) [9, 40, 41]
3) [sqrt5, 10, sqrt125]

Answer 1

To determine if a set of side lengths form a right triangle, we can use the Pythagorean theorem

Step-by-step explanation:

To determine if a set of side lengths form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Using the formula a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse, we can check if the given side lengths satisfy this equation.

1. [2, 2, sqrt4]: The lengths of the legs are both 2, and the length of the hypotenuse is √4, which is also 2. Therefore, this set of side lengths does form a right triangle.
2. [9, 40, 41]: The lengths of the legs are 9 and 40, and the length of the hypotenuse is 41. If we calculate 9² + 40², we get 1681, which is equal to 41². This set of side lengths does form a right triangle.
3. [sqrt5, 10, sqrt125]: The length of one leg is √5, the length of the other leg is 10, and the length of the hypotenuse is √125. If we calculate (√5)² + 10², we get 105, which is not equal to (√125)². Therefore, this set of side lengths does not form a right triangle.