Question

Select all the sets that are the three side lengths of right triangles.

1) 8, 7, 15
2) 4, 10, √84
3) 8, √11, √129
4) 1-√3, 2, 3-√

Answer 1

To determine which sets are the three side lengths of right triangles, we can use the Pythagorean theorem. The set of lengths 1-√3, 2, and 3-√2 is the only one that forms a right triangle.

Step-by-step explanation:

To determine which sets are the three side lengths of right triangles, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

1. For the first set of lengths, 8, 7, and 15, we can see that 8² + 7² = 64 + 49 = 113, which is not equal to 15² = 225, so this set is not a right triangle.
2. For the second set of lengths, 4, 10, and √84, we can calculate 4² + 10² = 16 + 100 = 116, which is not equal to (√84)² = 84, so this set is not a right triangle.
3. For the third set of lengths, 8, √11, and √129, we have 8² + (√11)² = 64 + 11 = 75, which is not equal to (√129)² = 129, so this set is not a right triangle.
4. For the fourth set of lengths, 1-√3, 2, and 3-√2, we can find (1-√3)² + 2² = 4 - 2√3 + 3 + 4 = 11 - 2√3, which is equal to (3-√2)² = 9 - 6√2 + 2 = 11 - 6√2, so this set is a right triangle.

Therefore, the only set that represents the three side lengths of a right triangle is 1-√3, 2, and 3-√2.