If the following sets are lengths of sides of a triangle, which set are lengths of sides of a right triangle?Select one:a.6, 8, 12b.3.5, 2, 4.05c.17, 8, 15d.1.5, 2, 3.5

To determine if a set of lengths can form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Let's apply this to each set:

a. 6, 8, 12: 6² + 8² = 36 + 64 = 100, which is not equal to 12² (144). So, this set cannot form a right triangle.

b. 3.5, 2, 4.05: 3.5² + 2² = 12.25 + 4 = 16.25, which is not equal to 4.05² (16.4025). So, this set cannot form a right triangle.

c. 17, 8, 15: 17² + 8² = 289 + 64 = 353, which is not equal to 15² (225). So, this set cannot form a right triangle.

d. 1.5, 2, 3.5: 1.5² + 2² = 2.25 + 4 = 6.25, which is not equal to 3.5² (12.25). So, this set cannot form a right triangle.

Therefore, none of the given sets can form a right triangle.