Classify the triangle based on side lengths 5, 7 and 8.. a. right. b. acute. c. obtuse. d. no triangle can be formed with given side lengths

The classification of the triangle is based on the relationship of the square of the longest side to the sum of the squares of the two remaining side. This is shown below,
                                 a² + b² ___ c²
Substituting the values,
                           5² + 7² ___ 8²
                                 74 > 64
Because of this relationship of the squares of the sides, the triangle is OBTUSE. Therefore, the answer is letter C. 

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