Final answer:
To determine whether a set of side lengths forms a right triangle, we can use the Pythagorean theorem. The set of side lengths that does not form a right triangle is A. 21, 220, 221.
Step-by-step explanation:
To determine whether a set of side lengths forms a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's check the given sets of side lengths:
A. 21, 220, 221: 21^2 + 220^2 = 529 + 48400 = 48929; 221^2 = 48961. The sum of the squares of the shorter sides is not equal to the square of the longest side, so this set does not form a right triangle.
B. 15, 112, 113: 15^2 + 112^2 = 225 + 12544 = 12769; 113^2 = 12769. The sum of the squares of the shorter sides is equal to the square of the longest side, so this set does form a right triangle.
C. 7, 20, 25: 7^2 + 20^2 = 49 + 400 = 449; 25^2 = 625. The sum of the squares of the shorter sides is equal to the square of the longest side, so this set does form a right triangle.
D. 13, 84, 85: 13^2 + 84^2 = 169 + 7056 = 7225; 85^2 = 7225. The sum of the squares of the shorter sides is equal to the square of the longest side, so this set does form a right triangle.
Therefore, the set of side lengths that does not form a right triangle is A. 21, 220, 221.