The correct classification for triangle ABC based on its sides and angles is option (b): "Obtuse, Scalene because AC = √17, BC = √53, AB = √68; AC² + BC² > AB²."
To justify this answer, consider the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (AB in this case) is equal to the sum of the squares of the lengths of the other two sides (AC and BC). The theorem is expressed as AC² + BC² = AB².
Given that AC² + BC² is greater than AB² (as stated in option b), it implies that triangle ABC is obtuse, as the sum of the squares of the shorter sides exceeds the square of the longest side. Additionally, since the side lengths are not equal, triangle ABC is scalene, not isosceles. Therefore, option (b) is the correct classification for triangle ABC.