Determine which set of side measurements could be used to form a right triangle. $5,3,6$ $5,12,14$ $12,3,17$ $12,20,16$

Step 1 ：We are given four sets of side measurements: \([3, 5, 6]\), \([5, 12, 14]\), \([3, 12, 17]\), and \([12, 16, 20]\). We need to determine which of these sets could be used to form a right triangle.

Step 2 ：To determine if a set of side measurements could form a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem 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 \(c\) represents the length of the hypotenuse, and \(a\) and \(b\) represent the lengths of the other two sides.

Step 3 ：Applying the Pythagorean theorem to each set of side measurements, we find that only the set \([12, 16, 20]\) satisfies the equation \(a² + b² = c²\).

Step 4 ：Final Answer: The set of side measurements that could be used to form a right triangle is \(\boxed{[12, 16, 20]}\).